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A FOUNDATION

FOR

ELECTRONIC MUSIC

2 ND EDITION

Roland

Contents Hi

Contents

Introduction v

Chapter One: What is Sound?

1-1 Introduction - • • 1

1-2 Sound 1

1^3 Pitch 1

1-4 Resonance in Air Columns 2

1 -5 Resonant in Strings 3

1-6 Timbre 4

1-7 Tone Color in Vibrating Air Columns 4

1-8 Tone Color in Vibrating Strings 5

1-9 Tone Color in Musical Instruments , , 7

1-10 Loudness • 8

1-11 Propagation of Sound Waves 8

1-12 Echo and Reverberation 9

1- 13 Spatial Effects 10

T-14 Questions 11

Chapter Two: Electronic Music

2- 1 Introduction 13

2-2 Live Electronic Music 13

2-3 Musique ConcrdtB 13

2-4 Recorded Electronic Music 14

2-5 Waveforms 14

2-6 Additive and Subtractive Synthesis 16

2-7 The Voltage Controlled Synthesizer 19

2-8 An Approach to Subtractive Syn^sis 19

2-9 Noise , 20

2-10 Computer Music 20

2-1 1 Direct Synthesis 23

2- 12 Questions 25

Chapter Three: Pitch

3- 1 Introduction , - ■ 27

3-2 Pitch Relationships in Music 27

3-3 Beat Frequencies 28

3-4 The Natural Harmonic Series 29

3-5 Consonance and Dissonance 30

3-6 Pitch Standard . .31

3-7 Exponential Progressions 31

3-8 Cents 32

3-9 Voltage-to-Frequency Relations - 32

3-10 The Linear V€0 33

3-1 1 The Exponential VCO 33

3-12 The Low Frequency Oscillator ....... ^ 36

3-13 Frequency Modulation 36

3-14 The SasJe Symhesizer Patch -36

3-15 Questions 38

iv Contents

Chapter Four: loudness

4-1 Introduction 39

4-2 Measuring Loudness ^ . 39

4-3 Frequency Response of the Ear 40

4-4 Dynamic Range ^-j

4-5 Intensity of Harmonics 42

4-6 Envelopes 44

4-7 VGA Control Response 45

4-8 Amplitude Modulation 47

4-9 The Basic Synthesizer Patch , , 47

4- TO Questtons 49

Chapter Five: Timbre

5- 1 Introduction 51

5-2 Noise . . . . i 51

5-3 Filters 51

5-4 The Low Pass Filter 52

5-5 The Voltage Controlled Low Pass Filter 55

5-6 The High Pass Filter 55

5-7 The Band Pass Filter and Band Reject Filter .57

5-8 Effeotsof Filtering on Waveforms 58

5-9 Resonance in Filters , 60

5-10 Ringing in Filters 64

5-1 1 The Ba^ Synthesizer Patch 64

5-12 Questions gg

Frequency Range Chart facing page 66

Metric Conversion Table and Metric Relationships facing page 67

Index 67

Introduction

As the title implies, the purpose of this book is to lay a
foundation for the study of electronic music, particularly
in relation to the voltage controlled synthesizer. Prxtical
Synthesis for Electronic Music (published by Roland) should
also prove useful to the reader. Through a series of practical
exercises it shows how theory can be applied to a particular
electronic music system. It also includes a step-by-step
example of recording electronic music using a synthesizer
and equipment found in most hi-fi systems.

With the advent of smaller synthesizer systems and semi-
professional studio equipment such as mixers and multi-
^annel tape recorders, the world of electronic music is no
long^ restricted only to large Institutions arnf organizations.
For the creative musician, this opens up a whole new world.
Not many unknown musicians get the chance to work
with an orchestt^ to try their own arrangements or original
impositions and the people at the record companies do
not have time to work through a score to mentally "hear"
what a new song sounds litce; they want to hear a demonstra-
tion tape. Besides, there are many things which go into 8
composition which simply cannot be written down on )Kq>er.
Budding young composers seldom get a chance to hear their
works performed by a full ort^estra or a large band^ and how
are they to learn the art of Instrumentation If they never hwr
the results of their efforts? By studyiiig ttia scoras of great
music? By analyzing the sounds on great records? That is
a little like studying great works of sculpture and then trying
to make a statue while wearing a blindfold.

The marriage of electronics and music opttis up a world
limited only by the musician's imagination. The synthesizer
can create all the sounds of conventional music and create
sounds never heard Isefore. But without at least a basic

understanding of acoustics and the synthesizer this world is
unapproachable. This book tries to give that understanding.

I would like to express grateful appreciation to my fellow
workers at Roland without whose help and patience this
work would have been impossible.

Robin Donald Graham
Synthesizer Project Manager
Roland Corporation

Osaka, Japan
December, 1978

What is Sound ?

1-1 Introduction

In dealing with methods for synthesizing sounds nnany texts,
including this one, seem to emphasize the imitation of
conventional musical instruments and natural sounds.
There is an important reason for this. All synthesis is based
on one simple principal: the building of sound from basic
elements. To understand these elements, we must understand
acoustics. If we learn to imitate sounds with which we are
^nintliar we are well ion the road to being able to syn^esize
any sound we can imagine, all the way from purely electronic
waillngs, blips, and bumps to the creation of imaginary
instruments, instruments which do not exist in the real woiid
but which sound as if they actually did exist somewhere as
acoustic instruments.

The purpose of this chapter is to provide that essential back-
ground \tt bmic acoustics.

1-2 Sound

Sound is what we experience when the ear reacts to a certain
range of vibrations. These iribrations themselves can also be
called sound.

Most soLind sources produce sound by means of some part or
parts which vibrate when rubbed, strucic, or excited by some
other means. Others produce sound by direct excitation of
the air as, for example, Ijlowinc] across the mouth of a
bottle to set the air inside vibrating thus producing sound.
Electronic instruments produce sound only indirectly; they
produce variations in electrical current which are normally
processed and passed through an amplifier where they
are made stroig enbu{^ to dHve a speaker. The vibrating
speaker cone then produces sound.

The three qualities of sound are pitch, timbre (tone color),
and loudness. It is the combination of these three qualities
that allows us to distinguish between different sounds.

1-3 Pitch

Pitch is that quality of sound which makes some sounds seem
"higher" or "tower" than others. Pitch is determined by the
number of vibrations produced during a given time period.
The vibration rate of a sound source is called its frequency;
^e hiigher Hie ^equency (or the hl^er the vibration rate),
the higher the pitch.

Tuning forks are used to produce accurate test pitches for
use in laboratories and for tuning musical instruments. A
close inspection will reveal that when a tuning fork is struck
on the surface of a piece of hard rubber, the prongs appear
slightly blurred due to their vibration. Dipping the vibrating
prongs Into a beaker of water will cause the water to be
violently ^itated.

In a similar way, the vibrating prongs of the tuning fork
agitate the air around them, sending out sound waves.

2 What is Sound?

1-4

This is shown in Fig. 1 -1 , When the prong moves to the side,
it compresses the air particles together. This disturbance of
air particles moves in such a way that a pulse of compression
travels away from the prong. When the prong moves to the
other side, it produces a rarefaction of air particles which
move outward simltarly.

It is important to realize that the Individual air particles are

only moving back and forth, transmitting the waves of
compression and rarefaction outward from the source.

The distance between any two corresponding points in
two consecutive pulses is called the wavelength (X). The

wavelength will depend on how fast the vibrations of sound
occur and the speed at which the waves travel.

The speed of sound in air may be given as approximately 331
meters per seccmd (or about 700 miles per hour). This speed
will vary slightly with the temperature and density of the air.
Neglecting these effects and assuming the speed of sound to
be consent* the wavelertgtfl will be directly related to the
rate of vibration of the source.

v = V

where: X = wavelength in meters

V = velocity of vound In meters per second
/ = frequency in vibrations per second

Thus the higher tile frequency of the vibrations, the shorter
the wavelength, the higher the pitch.

Frequency is often measured in units called the Hertz (Hz),
named kfter Heinrich Rudotf Hertz (1857-1894). If a sound

source vibrates at a rate of 100 vibrations per second. It Is
said to have a freciuency of 100 Hertz.

The frequency response of the ear, or in other words the range
of frequencies yiAt\dh can be heard^ will vary from person to
person. The average person can hear sound from about 20 Hz
to about 20,000 Hz. Some people can hear sounds as high as
25,000 Hz. The upper frequency limit will drop, however,
as a person gets older. For example, a person of 40 or 50
years of age may be able to hear only up to about 15,000 Hz
while In old age this may fall to 10,000 Hz.

Resonance in Air Columns

An analysis of pitch might begin with an Investigation of
r^onance. It is welt known that the best way to keep a child's
swing in motion is to give it small pushes in time with its
natural period of swing. This is a classic example of resonance.
The amount of energy exerted to keep the swing in motion
is quite small compared to the amount of energy available
from the motion of the swing.

RettMtancB occurs whenever a body or system is set into
vibration at its own natural frequency as a result of impulses
received from some other body or system vibrating at the
same fr^uency.

Fig. 1-1 Prodiigtioh of Sound Waves

Wave motion

Particle motion

n n

— Pressure

X - Wavelength

Fie> 1^ Examples of PIteh Ranga*
(See else chart facing p. 66)

20 Average hearing

20.000

1^.4 Large pipe organ

8.372

27.5 Grand piano

4,186

30.868 Orchestral music

3,951.1

1 I
The extremely low organ pitch is exptained in Chapter 5 tp. 57].

What is Sound? 3

1-5

Resonance with sound waves can be demonstrated by using
resonance tubes as shown in Fig. 1-3. By raising and lowering
a tube placed inside a tall container of water, the effective
length of the aif column Inside the tube is changed. Starting
with a very short air column, a vibrating tuning fork is held
over the mouth of the tube. As the tube is slowly raised,
resonance will o&iur when the air column reaches a certain
critical length and a relatively strong tone will be produced.
If the tube is raised mon, other resonance points will be
found.

Fig. 1-4 shows whythis happens. Assume that the lower prong
is moving down, as shown in (a). This will cause a pulse of
compression to travel down the tube which will bounce off
the surface of the water and return to the mouth. If the com-
pression reaches the mouth of the tube just as the prong
has reached its lowest position and is about to move upwards
(as in {fo)), the compression will be followed by a rarefaction
pulse which will also travel down the tube and reflect from
the surface of the water. Up to this point, the prong has
fihis*ied one complete cycle of wavelength of sound and
the sound wave {one compression and one rarefaction) has
travelled twice down and up the tube. It follows, then, that
the leng^ of the column Is one quarter the wavelength of the
sound. "I This is the principal which determines the pitch
produced by all sound sources which consist of a tube with
a closed end.

Resonance may also be obtained with a pipe which is open at

both ends, as shown on Fig. 1-5. In this case, the compres-
sions and rarefactions travel the full length of the tube
because there is no closed end to reflect the waves. The
length of the tube will be one half the wavelength of the
sound wave; or the wavelength of the sound wave will be
twice the length of the tube.^

Resonance in Strings

Three factors determine the pitch that a vibrating string will
produce: Its length, its mass, and ihe amount of tension

which holds the string stretched. As an example of these, the
guitarist changes the length of the strings by pressing them
against tiie frets to raise tfieir pitches; each guitar string is of
a different diameter, the lower pitched strings being thicker;
the guitar is tuned by adjusting the tension on the strings,
the tighter the string, the higher the pitch.

Experiments with vibrating strings may be conducted with an
easily constructed monochord (sometimes called a sononw-
ter), as shown in Fig. 1-6.

Fig. 1-3 Closed End RmonanceTube

■Glass or metal tubes

-Water

Fig. 1-4 Resonance in a Closed Tube

® ®

Compression
down and up

Rarefaction
down and up

Fig. 1-6 Open End Resonance Tube

Glass or metal
tubes

1 . In actual practice, if measurements are made, a discrepancy in the
tube length will be noted. This is due to the fact that the sound
waves produced at resonance actually extend slightty beyond the
open end of the tube as a result of air disturbance in this area. The
amount by which the wave extends is called end correction.

2, This statement neglects the slight deviation due to end correction.
(Since both ends of the tube are open, end correction occurs at

both ends).

4 What is Sound?

Resonance in a vibrating string can be demonstrated with a
monoGhord and a tuning fork. The simplest approach would
be to tune the monochorcT to unison wi^ the tuning fork
by adjusting the tension on the string and the position of the
bridges. If the unison is perfect, placing the stem of the
Vibrating tuning fork on the point of one of the inn^^m hear
the string will cause the string to vibrate. It is posslbis to
find other resonance points of the string by moving the
opposite bridge closer (witiiout hanging the tension on the
string) and noting ^e positions where string vibrates.

The frequency of the vibrations of a Stretched String is
inversely proportional to iu length. Assumingthe tension and
diams^ of the stringtemalhunchanged, if a string Of Hength
(distance between the bridges) produces a frequency of x
Hertz, then a string of I will produce a frequency of 2x
Hertz, a string of / will produce a frequency of 3x Hertz,
etc.

The thicker and heavier a string is, the lower its frequency
for a given length and tension. Thicker strings are usually
stiffer which means that the sound will die away rather
quickly, a feature not particularly desirable in musical instru-
ments. To achieve the necessary mass without loss of flexi-
bility, lower pitched strings are often wound with wire. This
can be seen by examining the strings of a piano or guitar.

It would be possible to present a similar discussion on the
relation of size, tension, and mass to the pitches produced
by other vibrating objects such as reeds, metal bars, etc.

Fig. 1-6 Monochord

Ideally, a pulley should be located here. For simple
experiments where accuracy is not too imporunt, the pulley
may be omitted, as shown.

1-6 Timbre

Timbre comes from French and means "tone color". In
English, we pronounce it: tarn' bar or: tim'bar.^

Timbre or tone color is that quality of sound which allows us

to distinguish between two sound sources producing sustained

sound at the same pitch.

Sound waves are the result of vibration. The vibrations of
most vibratory systems tend to be quite complex so that

they vibrate at several frequencies simultaneously. It is
the combination and interaction of these frequencies, called
overtones, which give a sound the quality we know as tone
color.

1-7 Tone color in Vibrating Air Columns

In 1-4 above, it was shown how acoustic resonant points

can be found using open or closed tubes and a tuning fork.
Starting with the air column at its shortest, if the tube is
slowly extencted inwe will be several points at vi^UA\ reso-
nance occurs. The first resonance point will be stronger than
the others with the next resonance points being progressively
lower in intensity. Using ^e child's svving as an motogy of
resonance, the secondary resonance points in the tubes
would be like giving the swing a push every other swing, or

3. a is in ^t;/ as in is; a ase in 490

every third, fourth, or fifth swing, and so on. From this. It
follows that if the impulses are not delivered every swing
(assuming pulses of equal energy), the swings will be of
lower intensity.

Since various lengths of air column will vibrate in resonance
to the one frequency of a tuning folic, it follows tiiat one air
column of fixed length will form resonances at several fra-
quendes.

Assuming that the length of an open end pipe is such that It
forms a resonance with the frequency of a tuning forte, the
vibrating prongs of the tuning fork will act as Impulses to set
the air inside vibrating. Since the tube is resonant at various
frequencies in addition to that of the foric, the Impulses
supplied by the fork will tend to cause the air inside to
vibrate at all of these resonant frequencies simultaneously.
These types of overtones are called harmonics because of
their muiriGaHy harmonic relation to eadi othw.

The lowest of these frequencies, or the fint harmonic, has a

vtfavelength equal to twice the length of the open end pipe 4
This frequency is usually the strongest and it is this frequency
whKbh gives the total sound its overall musical piteh. For this
reason, the first hannonie is also called the liindiumiital*

The remaining harmonics are all multiples of the first har^
monic or fundamental. The next higher harmonic is tfie
second harmoiilG with a frequency twice that of the funda-
mental. Following that is the third harmonic with a frequency
three times that of the fundamental and so on, theoretically
Upwards to infinity.

This series of harmonics is called the nitiml hannoiile

series. Most vibratory systems tend to produce harmonics,
but not necessarily all of the harmonics in this series. The
sound from a closed end pipe, for example, conteins only the
odd numbered harmonics. This is because for even numbered
harmonics, the portion of the wave being reflected from the
closed end is cancelled by fhB opposite portion of the wave
coming from the open end. The tone quality produced by a
closed end pipe, then. Is different from that of the open end
pipe; it contains fewer harmonics and thus Is a little duller.

Tone Color in Vibrating Strings

In 1-5 above, it was shown how string resonance can be
demonstrated with a monochord and a tuning fork. As with
a fixed length of air column, a string with fixed characteristics
will also be resonant at various frequencies, all of which fall
Wi^in tite natural harmonic series. In the above mentioned
string resonance experiment, if it were possible to obtain
several tuning forks, each tuned to one of the harmonics
of the first tuning fork, it would be seen that these fork^
would also cause resonant vibration of the string. As with ^ie
open end pipe, ^e vibrating string can produce all of tfie
harmonics in the natural harmonic series.

4. Neglecting and correction, as before.

6 What IS Sound?

Rg. 1-7 shows three of the vibratory modes of a string
(or three of the harmonics) as they would look if it were
possible to completely separate tiiem from each other. In
the fiindarnehtal mode of vlbratiion (a), nodes, or points of
minimum agitation, naturally appear at the ends of the string
since it is anchored at these points. In its next mode of
vibration (b), aribther node appears at the center bf the stnng.
Since this effectively cuts the length of the string in half, the
frequency produced by this mode of vibration is twice that
of the fundamental, br in other words, the second harmonic.
The next mode of vibration (c) adds another node which ef-
fectively divides the string into thirds, thus producing the
l^ird harmonic.

The tone cbtor etctuatly produced by a vibrating string will

depend on how the string is excited and at what point along
its length it is excited. Logic would dictate that a node could
not appear at the point bf exdtation. If the string is ptucked
or bowed at its center, it is impossible for any nodes (points
of rest) to appear at this point, thus, since all even numbered
harmonic$ produce nodes at the center, ihase harmonics
would be missing from the sound.

Antinodes,- or points of maximum agitation, for the second
harmonic occur at a point one quarter of the way from the
end of the string, as shovvn in Fig. T-7 (b). If the string is

excited at either bf these points, the second harmonic wIH
dominate the sound and any harmonic with a node ^ these
points Will be missirtg from the sound (or in other words,

the fourth harmonic and any multiple of the foLirth harmonic).
Since the fundamental has neither a node nor an antinode at
these points, it will be present, but weaker than if the string
were excited at its center. It is possible to supressthe funda-
mental entirely by lightly touching the second harmonic
nodal point (the center of the string) wtlh edge of a
card or feather, as shown in Fig. 1-8 (a). If the fundamental
is completely suppressed, the musical pitch of the string will
^em to be that of the second harmonic, since this Is nowthe
lowest harmonic present. Other harmonics may be obtained
with this same method using the related nodes and antinodes.
f\g. 1-8 (b) shows how to obtain the sixth harmonic. The
pitch produced will be two octaves and a fifth above the
missing fundamental. IVIost string instruments are excited
near one of the string, thus the sounds produced are
rich in harmonies.

A very similar discussion can be presented concerning the
position of the pickup in relation to the strings of an electric
guitar. The pickup detects ihe motion of the string pacing
back and forth above it and generates minute electrical
currents which electrically mirror the string vibrations.
Assuming all harmonics to be present in the vibrating string,
if the pickup is placed under the center of the string, it will
be in the position of the node for the second harmonic.
Since a node is a point of minimum vibration, the pickup will
detect very little, if any, of the second harmonic portion of
the string vibration. All haimonlcs with a node at this point
will be missing from the output of the pickup. Other pickup

Fig. 1-7 Modes of Vibration
0 Fundamental mode

N N N

AAA

i I i

N N N N

N = Node (Point of minimum agitation)
A - Antinode (Point of maximum agitnlon)

FiB. 1-S Producing Harmonics

® Second harmonic

® Sixth hamionic

positions will produce sound with different tone coloring.
This is the reason that many electric guitars have more than
one pickup.

The material with which a string Is made, and its diameter

will affect the tone color produced. Most string instrument
players are aware of this fact; they often have favqrite brand
name strings they prefer for use with their fnstraments.
Thicker strings will be stiffer and therefore will have difficulty
vibrating freely at higher frequencies. With thicker strings,
the higher harmonics tend to die away very quickly.

Tone Color in Musical Instruments

Up to this point we have been primarily concerned with

sources of vibration vtfhich produce sound, particulariy

vibrating air columns and vibrating strings. The body of a
given instrument also has a profound effect on the total
tone color produced by that instrument.

The solid parts of the body of aft instrument have their own
resonances which are very similar to those in the vibrating
string In that the frequency of these resonances depend on
the dimensions, elasticity, and tensions of the various parts
of the body. Many instruments such as violins, acoustic
guitars, and drums also contain air cavities which resonate
in ways similar to vibrating aJr columns. These body
and air resonances all interact with each other and the source
of vibrations so as to emphasize or de-emphasize different
overtones produced by the vibrating sound source, and In
some cases to completely cancel some overtones ar>d/or
add new overtones not present in the original source of
vibrations. This explains why two violins which look exaetiy
the same may still sound quite different. For example,
the wood used in the bodies may be different.

As an example of the factors which decide the tone color of
a musical instrument, let us consider briefly the factors
which in general affect all wind instruments. First is whether
1*»e air column is closed or open. Closed pipes cannot produce
even numbered harmonics. Next is the scale of the pipe.
This refers to the ratio of the length of the pipe to the
diameter of the pipe. The larger the scale, the more difficult
it is to produce the upper harmonics. Third is the shape
of the pipe. Fourth is the intensity of the wind pressure
used to produce the vibrations. Fifth is the method of
excitation; in other words, whether by air passing across an
edge, or by reed. Sixth is the nature and thickness of the
walls confining tha iBr celumn. And last Is the size and shape
of the mouth and related parts.

Bells and cymbals are good examples of instruments which
produce overtones that do not fall in the natural harmonic
series. In the case of the cymbals, these non-harmonic
overtones are so strong and numerous that they drown out
any existing fundamental so that it is impossible for the ear
to detect a specific musical pitch. Bells often contain enough
harmonic overtones that our ears can recognize a musical
pitch. The non-harmonic overtones are what give the sound
its metallic "clanging" tone quality and is typical of sound

8 What is Sound?

sources which use metal plates or bars as a source of vibra-
tion.

One other point in connection with tone color should be
meniSoned. The room Tn which a sound occurs will also

affect the tone color of that sound. The room forms an air
cavity with its own resonances which react to the sound.
Smaller rooms, such as the average IMng room, often have a
very strong effect on the sound produced in them. Especially
affected are the lower frequencies.

1-10 Loudnesi

The first thing that may come to mind concerning loudness
is perhaps dynamics (changes in loudness) in music. At first
glance, loudness as a qudlW of sound might seem rather
simple and not as important as tiie other two qualities, but

this is not so.

The loudness of a sound will vary during its production.
This loudness contour is edited the envelope of the sound and
often forms a very important clue as to the identity of the
sound. Fig. 1-9 shows two envelopes. In (a) is shown the
envelope for a single guitar note. As soon as the finger releases
the string, the sound jumps very quickly up to its maximum
loudness after which it begins to die away slowly. The actual
maximum sound level reached and the length of time
required for the sound to die away will depend on how much
force is used in picking the string.

In fig. 1-9 (b) is shown the envelope for a vocalized "ah"
sound. With the guitar sound the basic shape of the envelope
will remain unchanged; the only possible variation from this
basic shape would be to dampen the string before the string
vibration ceases. In the case of the voice, the envelope can
be altered considerably, depending on the intonation of the
singer or speaker.

The relative intensity or loudness of the overtones contained
in a sound also affect its tone color. The high overtones in a
cymbal crash, for example, are very strong, much stronger
than the lower overtones.

1-11 Propagation of Sound Waves

Sound spreads from the source in the form of a series of
expanding spheres. As ^e sound waves travel away from ^e
source, they become weaker in intensity. If we imagine a
square measuring one centimeter on a side drawn on the
surface of a balloon, we can see that the square will become
progresively larger as the balloon expands. As sound waves
travel away from the source, they must progessively cover a
larger area, thus the sound energy is gradually dissipated until
it finally becomes too small to detect

Fig. 1-10 shows what happens to sound waves when they
encounter an obstruction such as a wall. A part of the sound
Is reflected from the sur^fae. Note the relation between
the source of the sounds and the apparent source Of ■flie
reflected waves. A part of the sound striking the wall is
absorbed by the wall, and any sound whi(^ is not absorbed

Fig. 1-9 Envelopes

(a) Guitar envelope

Loudness ^^^'^^'^'*^''^*»i„^ ^^^^^^^^ ^

0 .05 .1 .5 1.0 1.S 2.0
Time (Seconds)

(§) Vowel sound "AH"

Loudness

0 .05 0.1 0.5 1.0 1.5 2.0
Time (Seconds)

Fig. 1-10 Propagation of Sound Waves

APPARENT SOURCE OF REFLECTED WAVES

SOUND SOURCE

What is Sound? 9

or reflected will be transmitted by the wall to the air behind

it.

The amount of sound reflected, absorbed, and transmitted
by the wait wfll depend on the materials used in its construc-
tion. Hard smooth walls tend to reflect a great deal of sound.
Shon/ier rooms and indoor swimming pools are good examples
of rooms with highly reffectiwe walls. Soft porus materials
tend to absorb sound. Heavy drapes and thick carpets are
good examples of sound absorbers. Thin walls tend to
transmit more sound than thicker walls. Most professional
sound studios use heavy thici< walls to prevent transmission
of sound into or out of the studio.

1-12 Echo and Reverberation

Echoes are produced when sound waves are reflected from a
hard smooth surface such as a wall or cliff. If a person
stands at a distance from such a hard surface and claps his/
her hands, the time elapsed before the reflected sound is
heard will depend on the distance to the surface. In order for
^e sound to be heard as a separate echo, it must be separated
from the original sound by at least 0.1 second {100 milli-
seconds). Assuming the speed of sound to be 331 meters per
second^ the sound must travel a total of about 33 meters, or
about 16.5 meters one way. If the surface is less than this
distance, the returning echo will not be distinct but will seem
to be a continuation of the original sound.

A sound emitted within the confines of a room will expand

from the source and bounce back and forth between the
walls, floor, and ceiling of the room. Remembering that
sound expands as a series of spheres, it can be seen that these
multiple reflections will soon become very complex. The
effect is that the sound will be reinforced and will seem to
continue for a time beyond the point when the ori^nal sound
source ceases emitting sound. This type of echo is called
reverberation.

Reverberation time is the amount of time required for the
sound reflections within a room to die down to a given level
after the source ceases emitting sound. The reverbera-
tion time of a room will depend on the reflective qualities of
the surfaces within the room and the placement of objects
in the room. Some experts are said to be able to judge the
size of a room merely by listening lo its reverberation charac-
teristics. Many performers have been disconcerted by the
seeming loss of carrying power they produce during a show
as compared to reheasals in the same hall when empty. The
audience and their clothing are good absorbers of sound.

Many people Wke to sing while taking a bath. Most bathrooms
have very good reflective qualities with long reverberation
times. The reverberations tend to reinforce the sound of the
singing so that even a person with a weak voit» sounds
powerful and dramatic in the environment of the toth.

In electronic music, it is important to differentiate between
echo and reverberation. Echo is the effect produced by
distinctly separate reflections of sounds. Reverberation is ^e

10 What is Sound?

effect produced by multiple reflections. In echo, the reflec-
tions can be easily heard as separate repetitions of the original
sound evefi when Ijiey overlap. This is the familiar echo
effect obtained by shouting in the mountains. In reverbera-
tion, the reflections are blurred together so tiiat distinct
repetitions are not heard, but ratiier the orfgiriat sound sMitis
to continue longer than normal.

1-13 Spatial Effects

In electronic musib, most sounds start out as electrfcat vibra-
tions generated and controlled by the synthesizer and related
studio equipment; therefore, it is usually quite "dead"
sounding when put through a speaker. An artlffdti wiviron-
ment must be added to the sound to give it life. This is one
of the concepts of spatial effects.

The most importanteffect in electronic music is reverberation.
Wl^ reverberation we can create the feeling of intimacy felt

with ;i chamber orchestra in a small room or the feeling of
overwhelming power produced by the pipe organ in a large
cathedral. The amount of reverberation controls the size of
the space in which our electronic performance seems to take
place. Not only that, but we are not limited to a one size
"room''. We can change the apf>arent size of the space at
will so that it matches the mood of the music at each moment.

Reverberation can also be used to control depth or distance.
The person who sits in the front row at the concert hall hears
mostly the sound received directly from the instruments,
while the person in the last row will hear more of the rever-
berations than the direct sound (assuming speakers are not
used). This gives a due to the control of dfstan» in electronic
music. A melody played very softly with a great deal of
reverberation added will sound very distant from the listener.
A melody played loudly with little reverberation will sound
very close to the listener.

Besides special effects, echo can add complexity to music by
giving slightly delayed repetitions of sounds. When used with
sus^lnlng sounds such as string sounds. It can also add a

great feeling of depth. The late repetition of these delayed
sounds gives the effect of a much larger group of instru-
ments.

When a group of musfetans (or singers) ptay in unison to-
gether, they will each be playing a slightly different
pitch. This is one of the clues that tells us that we are listening
to a group rather than a solo. Units designed to getmate
chorus effects process the sound by altering the pitch slightly,
then re-combining this with the original sound to give the
effect of a group of players.

P\\am i^lfHng is another common effect used In dectronic

music, but the actual effect on the sound processed by a
phase shifter is very difficult to describe with words. One
deseriiption >nih\t^ o^es Mriy eUtxmt however, is to compare
phase shifted synthesi^r ni^ia outputto the sound produced
by a jet plane which hl^ just talcen off and is moving into the
distance. Phase shifting is an effect which is also common
with acoustic instruments and electric guitars.

What is Sound? 11

1-14 Questions

1 . What are the three qualities of sound? Define them.

2. Aiming the speed of sound to be 330 meters per second, what is the wavelength of a sdund wave with a
frequency of 440 vibrations per second?

3. What is the frequency response of the ear in the normal average human being?

4. Define resonance. Give examples of resonance which occur in daily life.

5. List three factors which affect the pitch produced by a vibrating string and show how changes in each will
affect the pitch.

IB. Mow are otferton^ produced and how do they affect the sound?

7. Define envelope. Give some examples of familiar sounds and make diagrams showing the approximate

envelope of each.

8. What three things happen when a sound wave encounters an obstruction such as a wall. Make a sketch showing
this.

9. What Is the difference between echo and reverberation?

10. Exi^aln how reverberation can be used to control the apparent distance between the sound and the listener.

Words to define:

antinode

edhio

env^lQpe

frequency

fundamental

harmonics

Hertz

loudness
monochord

natural harmonic series
node

non-harmonic overtones

overtones

pitch

rarefaction
r^sonan^
reverberation
sound

soundwaves
spatial effects
timbre
tDn$ color
wavelength

Electronic Music

Chapter TWo

2-1 Introduction

Throughout the ages composers have strived to break the
bonds imposed by Iheir art. A study of musical scores will
show how again and again composers have tried to break
away from the conventions of their times in search of newer
avenues Of expression. The use of newer hamiionfe structure
and the invention of new instruments all came about as a
result of this search. It is not surprising, then, that the
discovery of electricity should usher in the developement of
non-acoustic instalments.

This text deals primarily with electronically generated
(synthesized) sound. In electronic music we are not so much
concerned w1l^ sound sources, but more with sources of
electrical signals (or waveforms) which, when processed and
passed through an appropriate amplifier/speaker system,
become sound. We cannot, however, exclude tiie electronic
processing of acoustic sound sources. Picking up sound
with a microphone and passing it through an amplifier/
speaker system is, tef^ntcally speaking, electrorrio processing.
For this reason it sometimes becomes quite difficult to draw
the line between electronic music and non-electronic music,
especially since electronic music often uses acoustic sound
sources ~ sometimes with no alteration of the original sound
quality.

In this chapterwe shall look very briefly at some of the forms
electronic music takes and explore methods for synthesizing
sounds on a synthesizer.

2-2 Live Electronic Music

One form of live electronic musie invdvet ^e use of a un-
recorded tape of electronically processed or generated sounds
which is played on stage where one or more "live" solo
instruments play in counterpoint to the tape. Another form
of live electronic music involves the use of one or more
synthesizers; the smaller stage type or sometimes the larger
studio type. This type of music may or may not tneludftHip
use of a pre-recorded tape. Acoustic instruments may also be
involved. It is common to use human voices in their natural
form and/or processed electronically. Stage acticm may be
a part of the performance, as well as special lighting effects,
including the use of lasers.

2-3 Musique Concrete

In musique concrete, portions of tape recorded sounds are
cut up and patched together in different ways to form the
finished composition. Many times the portions are altered
before editing into the final composition. Among the many
changes possible are abrupt stopping and starting of a sound,
drastic or subtle changes in speed, playing the sound back-
wards, filtering, or any combination of these. Any sound
which can be recorded on tape becomes a candidate for this
art form. Considered from this point Of view a taipe recorder
can be thought of as a musical instrument Wfi^ as many
creative possibilities as any other musical Instrument.

14 Electronic Music

Although the subject of musique concrete is not delt with in
any detail in this book, its importance cannot be overlooked,
in the eiatly days of electronic music, musique concri^ was
considered to be a completely different form of music with
no relation to music generated with electronic oscillators, but
today this is not so. Indeed, musique concrete techniques
often form an integrated part of synthesizer generated
electronic music, and synthesizers are often used as sound
sources and sound modifiers in musique cwwriite.

2-4 Recorded Electronic Music

In most forms of electronic music the final product Is a
recording. In almtwt alt of these cases It vroutd be impossible

to hear this recorded music in any other form. This type of
electronic music usually involves tiie use of a multichannel
tape recorder or the use of ordtrtary taps recorders in a

fashion which imitates multichannel recording techniques.
Usually, each voice in the composition is synthesized and
recorded one at a time; This is very much like the process

involved if we tried to record a symphoney by having each
musicians come into the studio one at a time to record his/her
part

2-5 Waveforms

The tuning fork is an example of a sound source vMldh
vibrates only as a whole; therefore, it produces only the
fundamental and no other harmonics. This sound is very
clean and pure. If we could watch the movement of one of
the prongs and graph this movement, we would get a diagram
like that shown in Fig. 2-1 (a). The vibrating prongs of the
tuning fork cause minute changes in air pressure, tf these air
pressure changes were diagrammed, they would appear as
shown in (b). tf we placed a microphone near the vibrating
tuning fork, it would generate minute variations of electrical
current whose voltage changes would be as shown in (c).
An amplifier could be connected to the microphone and used
to drive a speaker* The moving cone of the speaker would
produce changes In air pressure which, assuming perfect
equipment, would exactly mirror the air pressure changes
origtnalty produced by the tuning fork. The only difference
would be that air pressure changes produced by the speaker
could be larger (amplified) or smaller (attenuated) than the
air pr^ure change reaching the microphone, depending on
the position of the amplifier volume control.

The three diagrams shown in Fig. 2-1 represent the waveform
of the sound produced by the tuning fork. The only dif-
ference betvifeen these waves Is the medium; in ^er words
(a) is the movement of a prong, (b) is air pressure changes,
and (c) is voltage changes. In electronic music, of course, we
are usually more concerned with ihe medium of voltage
change.

The waveform produced by the tuning fork is called a sine
wave. Imagine a pen attained to the end of a pendulum. If
we tAae» a ler^ of pt0st under tiie pendulum in such a way
that the pen remains in contact with the paper and if we pull

Fi«.2.1 WBVSfbrms

® Movement of one prong

Pitch = 440 Hz A

Left
Rest

Right

one wavelength

Appro x"*^ —

,0023

440 CyclB

s = 1 Second

Time for _ 1 Second
one cycle Frequency

® Air pressure changes as a result of tuning fork vibration
+ Pressure

Normal
air

pressure

—JQ073

Mcond

— Pressure

Q Voltage generated by microphone (fricklng up tuning fork)
+ Voltage

Voltage

■ .0023

second

Fig. 2-2 Wavefomrts in an Audio System

Prong Air

movement pressure Voltage

Cone Air
Voltage movement pressure

AmpVtfieT

9 000 O

Electrantc Music 15

the paper at a steady rate of speed as the pendulum swings
the pen will draw a perfect sine wave, as shown in Fig. 2-3
Sine waves are mathematically very closely related t^ the
circle and they are very easy to generate using mechanical
means that are based on the principle of the wheel. Ordinary
hons^old elei^iGfty Is generated wJth machines which spin
and thus produce current in the form of a sine wave Most
courttrles use either 60 Hz or 50 Hz for household electricity.
60 Hz produces the apprcwimate pitch of B below the bass
cleft, while 50 Hz produces the approximate pitch of the A
tJbelow that. If we had tuning forks which could produqe
these pitches, the only difference between the sound of these
tuning forks and the sound which could be produced by
an ordinary house current would be one of intensity The
sound of the tuning fork would also gradually die away.

Since the complex vibration modes of different types of
sound sources produce sounds with a different harmonic
content, each type of sound source wfll produce Its own
unique waveform. A few waveforms are shown in Fig. 2-4

Fig. 2-4 Waveforms
© Flute

Pitch = D4

Pitch = G3

Pitch = D4

Pitch - F4

Spectrum Diagrams
Pitch = D4

-40

•I-

r'l-

Pitch = G3

Frequancy

-30

-40 1

100

Pitch = F4

300

500 11

Frequency

4° I

-30

-40 1

Frequency

16 Electronic Music

With each waveform is shown a spectrum diagram. Spectrum
diagrams show the harmonic content of a sound or waveform.
Frequency is shown atong the bottom of each diagram. Each
heavy vertical line represents a harmonic and the length of
each line represents the relative amount of that harmonic
which is contained in flie tof&t sound. In synthesizing sotiiids,
spectrum diagrams will often prove much more useful than
drawings showing waveforms. Waveforms are sometimes
helpful, however, as seen with the flute waveform which is
close to a sine wave indicating that the flute tone quality
contains relatively few, low-intensity harmonics.

Additive and Subtractive SyifHiesis

In electronic music there are two basic approaches to synthe-
sizing sounds: additive synthesis and subtractive synthesis/'

In additfve synthesis we start with sine waves of various
frequencies and add them togatfier in the correct amounts to
produce sound with the desired harmonic content. This
method usually requires a large number of sine wave sources
(one for each harmonic desired). The harmonic content of
many sounds changes during its production, thus the
accurate control of the amount of each indhfidual sine wave
becomes quite compfex. For these reasons additive synthesis
is not as common as subtractive synthesis, hut oven so, it
is sometimes used to a certain extent with synthesizers
designed for subtractive synthesis.

In subtractive synthesis we start with a waveform which is
already rich in harmonics and use electronic filters to remove
unwanted harmonics to produce the desired sound. In place
of the vibrating air column, string, mat&l plate, etc., we
use an oscillator (electronic waveform generator) which is set
to generate a waveform rich in harmonics. The output of
the oscillator is connected to a filter which alters the basic
tone coloring in ways not unlike the effects of the body
of a musical instrument. In many cases, one filter is enough
to easily synthesize at least passable imitations of many
sounds, but it is usually advantageous to use several fitters to
help imitate more closely the physical characteristics of the
body of the instrument and the changes which occur during
the production of each note. The oscillator, then, would
be analogous to the vibrating portion of an instrument and
the filter analogous to the body of the instrument.

In subtractive synthesis, two of the more common waveforms
are the sawtooth (or ramp) wave and the square wave, shown
in Fig. 2-5. A glance at the mechanical symetry of these
waveforms will hint at the fact that they are very simple to
generate electronically. For example, a square wave can be
generated very simply with a circuit which continually turns
itself on and off. It is also easy to accurately control the
frequency of such wave generators, this being an important
consideration for accurate pitch control in music. The
exactness of these waveforms also gives a hint of the regularity
of the harmonic content of each, as shown in the respective
spectrum diagrams.

1. This discussion diitfesBfds cSract synthesis by computer which is
presented later in tliis diapter (2-1 1 ; p. 23).

Electronic Music 17

Fig. 2-5 SYNTHESIZER WAVEFORMS

HARMONIC SPECTRUM
OF PERFECT SAWTOOTH
WAVE

-10

-20

dB -30

-40

-60

HARMONIC NUMBER i
FREQUENCY x

2
2X

4
4X

6 7 8 9 10
6X 7X 8X 9X IIK

HARMONIC SPECTRUM
OF PERFECT SQUARE
WAVE

-10
-20
dB -30
-40
-50
-60

HARMONIC
FREQUENCY

5 7 9 II 13 IS 17 19
5X TX 91C II X 19X

18 Electronic iVlusic

In Fig. 2-6 (a), three sine waves representinn the frequencies
X, 2x, and 3x (in other words, the first, second, and third
harmonics) are added together, the result of which looks
much like a sawtooth wave. If more harmonics were added,
the result would be a more perfect sawtooth wave. The
perfect sawtooth wave (Fig. 2-5 (a)), #ien, contains harmonies
which extend theoretically upwards to infinity. In Fig. 2-6
(b), three sine waves of frequencies x, 3x, and 5x (odd
numbered harmonics) are added together witfi the result
looking much like a square wave.

The sine wave and square wave are exactly symmetrical, both
horizontally and vertically; the wave patterns continually
repeat tfiennselves, and if they are inverted, i}tey look and
sound the same, as shown in Fig. 2-7. When inverted, only
the phase, or starting point, is different. Notice that if
wavefonns (a) and (b) are added together, tiie reujit Is zero,
or no sound. The same Is true of wa>»^rms (g| and (d).

The sawtooth wave may seem vertically imsymmetrical
because it looks different when inverted; the ramps go up
instead of down. Fig. 2-8 {a) shows w^at happens when we
add three inverted sine waves of frequencies x. 2x, and 2x.
Since the sound of a sine wave does not change when it is
inverted, we might expect that adding inverted sine waves
together would not produce a sound different from that
obtained by adding non-inverted sine waves, and this is
exactly what happens. The sound of the inverted sawtooth
wave and the sound of the non-inverted sawtooth wave are
exactly the same. For this reason, it is not important whether
a synthesizer produces upifoing or down-going ramps as a
source for sawtooth waves.

In Fig. 2-6, all harmonics are in phase with each other. In
other words, at the point where the harmonics all cross the
center "0" line at the same time (as they do at the beginning
of the periods diagrammed), they are moving in the same
direction: up. In Fig. 2-8 (a), they are all moving down.
Fig. 2-8 (b) shows what happens when we try to make a
square wave with odd numbered harmonics, but invert one
(the third harmonic) so that it is out of phase with the others.
"Oie important point here is that although the resulting
waveform does not look anything like a square wave, it
contains exactly the same harmonics as the wave in Fig. 2-6
(b), thus it will sound exactly the same. The tone color
of a sound source, then, will depend on the harmonic con-
tent of that sound and will usually have no illation to the
phase relationships of those harmonics except in sound
sources where the phase relation is in constant change (an
effect produced by a ^ase ^ifter}^ Thts is why spectrum
diagrams are usually more useful ^an knowing the waveform
of a sound source.

Even so, in some cases knowing the waveform of a sound
$oun» can be helpful, as with the Hute example cited in 2-5
above. Another example is that of the clarinet, whose wave-
forms are shown in Fig. 2-4 (b). These waveforms are clearly
quite near a siquare wiave and diej^ir^ tiie spectfum diagram
reveals that tiie odd numbered harmonics are stronger than

Ffitr. 2-S Addttion of Hennonics

Spectrum

1 2 3
Perfect saMttooth

1 2 3 4 5
Perfect square wave

Fig. 2-7 Inversion of Waveforms

Electronic Music 19

the even numbered harmonics. This, and the shape of the
waveforms, suggests that the square wave would be a good
place to start in synthesizing a clarinet. This is borne out by
the fact that the perfect square wave already sounds much
like a clarinet without any processing. Note that the wave-
forfns for ^e two pitches shown are a little different, indi-
cating that ^e tone color of the instrument changes with
pitch.

The Voltage Controlled Synthesizer

All voltage controlled synthesizers are basically alike^ Tfi*
main differences are the package, the number of elements
or modules available for synthesis, i^e number of communis
tion points between the musician and the internal circuits,
and the sophtsticstion of the circuits. The principals of syn-
thesis remain the same for all synthesizers.

Voltage control is based ott the eonc^Dt of modulation: the

control of one parameter by another. Most sound sources
produce sound which is quite complex. During the production
of only one note, many acoustical events may take place.
The most common are changes in loudness (the envelope)
and changes in the harmonic content of the sound. Most of
these events occur much too rapidly for them to be TOntrol-
led manually. This is where voltage control comes in. If we
know exactly how a parameter (such as loudness or harmonic
content) will react to a $peciffc voltage change, it is often
relatively simple to provide controlled voltage changes
which will produce the exact effect desired. With systems
which allow free interconnection of the synthesizer elements
(patching), another advantage of the concept of voltage con-
trol is that it is possible to connect any element output to
any other element input, thus providing a tremendous
variety of possibilities in synthesis.

An Approech to Subtrectiva Synthesis

The synthesis of sound is an art In itself. The most important
ingredients to its mastery are patience and practice; practice
particularly in the sense of familiarity with the synthesizer
controls and their effect on the output sound.

Fig. 2-9 shows the basic patch or connection of the three
basic synthesizer element which are the most closely related
to the three qualities of sound: pitch, tone color, and foud-

ness. As shown, the arrangement is relatively useless because
there are no control (modulation) inputs. These will be
added in later chs^iters.

The voltage controlled oscillator or VCO is the basic Source

of pitch. An oscillator is simply an electronic circuit which
generates electrical waveforms. The frequency or pitch of
these waves is controlled by means of a control voltage.

The most obvious source of pitch control voltage would be

a keyboard, but there are many other possible sources.

Fig. 2-8 rn\wrsion of Hsrmoitks

(a) All inverted (b) Third harmonic inverted

(Sawtooth ) (Square)

-f- ■¥

spectrum Spectrum

Fig. 2-9 The Basic Synthesizer Patch

Pitch Tone color Loudniess

Pitch Tone color Loudness

control control control

input input Input

The voltage controlled filter or VCF is the basic element
concerned wi:^ control of tone color. A filter is an electronic
circuit which is able to remove or accent desired frequencies

20 Electronic Music

or harmonics in a sound source. The particular frequencies
or harmonics acted on can be decided by means of a control
voltage. The advantage of voltage controlled filter character-
istics is with sounds in which the harmonic content changes
during the production of a note and for creating the tone
color ehangiBs in thoiiB sounds vMdh are pdrticulaHy asso-
ciated wilti the synthesizer.

The voltage controlled amplifier or VCA is used to control
the articulation of the sound by means of a control voltage.

Of the three qualities of sound, pitch and loudness usually
present little problem in synthesis. If we want to synthesize

a piccolo or a pizzicato string bass, it is extremely simple to
decide and set the correct pitch range, and by repeatedly
pressing a key on the Iceyboard while adjusting the loudness
related controls, we can easily arrive at the correct envelope
for the desired sound. Tone color is a different matter,
however, and often requires much trial and error no matter
how logically it is approached. This is where practice and
patience will pay off. Tone color is also strongly affected by
pitch and envelope or loudness. For^ese reasons, it is usually
best to approach the synthesis of a specific sound by first
deciding and setting the correct pitch range, then the correct
loudness contour or envelope. Once these qualities of sound
are more or less correct, it is possible to approach and
experiment with tone color.

2-9 Noise

The VCO forms the basic SOWld source for synthesizing
pitched sounds. Most syntfiesizers also include another
source of sound called the noif generator whidi Is used for
synthesizing non-pitched sounds. Usually, two types of
noise are provided: white noise and pink noise. White noise is
the random combination of all frequencies and produces
a hissing sound much like that which can be heard when an
FM radio tuner is set between stations. Pink noise contains
fewer higher frequencies and produces a rushing Sound much
like a waterfall. Noise is discussed in a little more detail in
Chapter 5 (p. 51 ). Fig. 2-10 shows a noise waveform.

2-10 Computer Music

The computer is becoming more and more common in the
production of electronic music. Many of the fi rst experi ments
involving computers and music were aimed at trying to have
computers "compose" music, thus the term computer music
may often be much misunderstood. This approach is no
longer common.

The use of computers in music more recently (an be divided

into two basic categories:

1. The use of computers to completely or partially con-
trol a synthe${:»r.

2. Dir^ syntiiesis in which a computer is used to generate
any desired wave^nm.

Fig. 2-10 Noise Waveform

Before discussing these two categories, it might be well to

Electronic Music 21

look at the question of why musicians would want to use a

computer in music.

At best, the score is only a poor representation of the musical
sounds the composer/arranger intended, and, therefore,
must be translated or interpreted. Fig. 2-11 illustrates this
process.

Fig. 2-1 1 Translation of Score into Sound

SYNTHE-
SIZER

COMPUTER

INSTRU-
MENT

PLAYER

MUSIC (SOUND)

INSTRU-
MENT

PLAYER

INSTRU-
MENT

CONDUCTOR

COMPUTER

(DIRECT

SYNTHesiSI

SCORE

COMPOSER/ASftANGER

Normally, the conductor interprets the score. In one passage
the horns should be louder than the other instruments, and
in another the music should slow down with these notes being
held a little longer than the other notes, and so on. During
the actual performance, the conductor can normally use only
body motions to remind the players of what is desired of
them. Even in the best of bands and orchestras there will
be some loss as the music filters down through each player to
the instruments, and thus finally emerges as sound. Using
a computer, the composer/arranger may translate music into
sound without the need to filter it through a group of
people.

It is a simple matter to translate a score directly Into com-
puter data for the production of music, but the result
would be very mechanical sounding. The result would be the
same if a conduetor conducted the score without trying to
interpret it in any way, except that the computer could
produce more accurate timing. It is very important for the
musician who uses a computer to interpret the music and
incorporate these interpretations into the computer program.

Returning to the two categories in which computers are
used, in the first category a computer is programmed with

22 Electronic Music

numbiers whf€^ represem ^ voltage lev^ pul$e -Uitiings
desired by the musician for the control of an ordinary
voltage controlled synthesizer. The computer, in effiBct, takes
the place of the keylx>ard controller or other controllers used
vvith tiie synthesizer.

Most electronic music is recorded one melody line at a time,
hence it is very difficult to judge how the different parts
will sound when mixed together. The result is often unac-
ceptable and some or all of the parts must be recorded over.
Computers offer a large advantage in this area since they can
be pFognenmed to provide simultaneous control of several
melody lines thus allowing ^e musician to hear how the
combination will sound.

Within the category of computer controlled synthesizers are
two approaches. The first is to use a standard computer
system in which a special "music" program would hgve to
be written and implemented. This requires an intimate
knowledge of computer programming which becomes one
of the major drawbacks of this approach. The other major
drawback is that it would usually be necessary to design and
build custom interfacing units in order to convert the com-
puter outputs into control voltages and gate pulses which the
synthesizer can use. If the musician is not interested in
learning enough to do this, he/she might be lucky enough to
enlist the aid of a computer hobbyist. The larger of the home
computer systems is capable Cif hendling a rather sophisticated
music program which would make it quite easy for the
musician to use. The smaller of these systems would also be
capable of music programs, but would be rather tlniitad In
what they could do and would probably require a rather
specialized music encoding procedure.

The second approach to computer controlled synthesizers
Would be fo use a specialized computer which hes been
designed so that its sole purpose is the control of a synthesizer.
The Roland IVlC-4 MicroComposer is the first example of
this type bf computer to be put on the market It uses a
simple encoding system which was first developed by com-
poser Ralph Dyck for use with a programmable digital
sequencer which he built for his commercial studio in
Vancouver, Canada.

The fundamental difference between the MicroComposer and
a digital sequencer, programmable or otherwise, is that the
MicroComposer was designed around an integrated Circuit

called a microprocessor or CPU (Central Processing Unit).
It is the microprocessor which is responsible for the versatality
of the MicroComposer. Since the MicroComposer was
designed with the musician in mind, it requires no knowl-
edge of computers or computer programming. It pro-
vides control for as many as eight melody lines plus as
many as six percussion voices, all completely independent
of each other. Its operation is very much like that of an
electronic desk calculator and, due to the use of a micro-
processor, the MicroComposer provides a great number of
operating functions which give the musician an unprecedented
amount of contral over the music betng produced. To produce
a similar amount of cormol in a home type computer would

Electronic Music 23

require a rather large system and sophisticated programming
techniques.

2-11 Direct Synthesis

In the second category of computers used In music, a series
of numbers whii^ represent the instantaneous values of
voltage levels at different points fh a waveform are stored In
a computer memory and called forth as needed to produce

sound. This is direct synthesis.

It is easier to understand direct synthesis by first demon-
strating how a waveform can be analyzed and stored in a
computer as data. This is done by sampling the sound wave
at regular closely spaced intervals. Each sample would
represent the instantaneous voltage level of the sound wave at
the sampled time. Each of these voltage values is converted
Into a number which is then stored in its own space in the
memory. This Is shown In Fig. 2-12 (a).

Fig. 2-12 Direct Synthesis
® Wave sampling

WAVE:

VOLTAGE LEVELS ATSAMPLED TIMES:

+10-

+5-

Level 0

-5-

-10-

MEMORY
DATA:

Ti=0

Ta -4^
T3 =+6iO
T4 = 47.0
Ts = +8.7
Tfi = +9.7
T7-+10.0
Tg=+9.7

+10-

+5-

-5-

-10-

15 20

(b) Wave generation
VOLTAGE LEVELS:

+10-

+5-

STORED
DATA:

T, =0
T2 = +2.6
T3 - +5.0
T4 *+7.0

Ts = +8.7
T,, = +9.7

= +10.0
Tg = +9.7

etc.

WAVEFORM:

-10-

+10-

+5-

-10-

ete.

24 Electronic Music

To retreive the sound wave, the computer reads the stored
data in the memory much as a person might run a finger
steadily down a column of figures. As each number is read,
it is converted into its corresponding voltage level. Each
voltage level is held until a new level comes along. The total
result Is a sound wa^ whfdi Is squared off; It has only hori-
zontal and vertical lines, no slants or curves. A filter is used
to smooth these corners off. This process is shown in Fig,
2-12 (b).

First, It can be seen that the sannpling rate would have to
be rather fast compared to the sound wave. The more samples
taken, the more closely the reproduced sound wave will
resemtile the original. There is a definite upper limit of
sampling speed which each computer can handle.

Second, there will be a limitation to the numbers available
for showing voltage levels. In the example shown In Fig. 2-12,
if the computer cannot haindle the digits to the right of the
cecimal point, the data for the sine wave would have to be
rounded off and written:

= 0

Tft =10

= 3

T, =10

= 5

T„ =10

= 7

Ts =9

= 9

T,o =7
ETC.

Thus it will be less like the original sine wave than the

original example was, as shown in fig. 2-13.

Since numbers representing the waveform are stored in the
computer memory, it becomes a very simple matter to
alter the wave by altering the numbers. From this it can be
seen that it is possible to invent any waveform and convert
it to data for loading into the memory. This is direct synthesis
which can exactly imitate any known sound, or can create
completely new sounds.

The major disadvantage of direct synthesis is that it requires
an extremdly targe computer system and Is thus limited to

large institutions. It aiSO requires an intimate knowledge
of computers and programming, including advanced mathe-
matics.

Fig. 2-1 3 Dfstprtlon in Dirw^ Synthesis

+10-

-10-

+10-

+ 5-

-10-

Major
□Utortlon

Electronic Music 25

2-12 Questions

1 . List sorne of the forms which electronic music can take.

2. Draw a sine wave. Explain this drawing in terms of air pr^sure changes. In terms of variations of electrical

current.

3. Explain additive and subtractive synthesis. Which is more common? Why?

4. What are two commonly used waveforms in subtractive synthesis? Why are they good for subtractive synthe-
sis? Give the harmonic content of each.

5. What effect does inverting a waveform have on its tone color? What effect does inverting some of the har-
monics in a sound have on ^e waveform? On the tone color?

6. What is the advantage of voltage control in a synthesizer?

7. In vi^at ways are a stage type synthesizer and a large studio system synthesizer different? In what ways are
they alike?

8. What are the three qualities of sound and what are the synthesizer elements most associated with eac^?

9. Generally, in which order should thethree qualities of sound be considered when synthesizing a sound? Why?
10. What are the two categories in which computers are used in electronic music?

Words to define:

additive synthesis
computer music
direct synthesis
electronic music

modulation
musique concrete
ndse

noise generator

oscillator

phase

pink noise

sawtooth wave

sine wave

spectrum

square wave

subtractive synthesis

synthesis

VGA

VCF

vco

voltage controlled amplifier
voltage controlled filter
voltage controlled oscillator
voltage controlled synthesizer
waveform
white noise

Pitch

Chapter Three:

3-1 Introduction

The first quality of sound which we shall discuss in detail is
pitch. Pitch is that quality of sound in which some sounds
seem higher or lower than others. In the voltage controlled
synthesizer, the mainsource of pitch is the Voltage Controlled
Oscillator or VCO.

One of the most common sources of control voltage for tfie

VCO is the keyboard controller. The keyboard controller
is nothing more than a voltage divider; the level of the voltage
output depends on which key is pressed. When the control

voltage is applied to a properly calibrated VCO, the VCO
will generate a pitch which is related to the key pressed.

In order to better understand the relation between the
frequency output of the VCO to tfie voltage input, it is
necessary to review the construction of our musical scale
system.

3-2 Pitch Relationships in Music

In music, instead of frequencies, pitches are given letter
names or syllable names, or sometimes numbers.

) ^ „ o ■■ °

CDEFGABC
DO RE Ml FA ^ LA Tl DO

1 2 3 4 5 6 7 8 (or 1»)

When more than one note is sounded together, this is called a
diofd.'' The tssult we hear as harmony. Different chords
produce harmony which to our eai% has different qualities.

The distance between two pitches is called an interval. The
two qualities of an interval are: consonance and dissonance.
A consonant interval (sometimes called a concord) is an
interval which to our ears seems to be harmonically at rest
or comfortable. A dissonant interval (sometimes called a
discord) is an Interval which seems jarring to our ears and not
harmonically restful.

It is possible to play a number of intervals and have a group
of people judge in which order they shcnild be placed so that
u^en flayed they would move gradually from consonant

to disson^ant. Somewhere near the middle of this progression
would be a dividing line between consonance and dissonance.
The postfton of thfs dividitig line has changed over the years

so that chords which we consider consonant now would
have been considered dissonant in the earlier periods of
muiic.

The interval which causes the least amount of jarring when

it Is heard is unison: two pitches of exactly the SEime fre-
quency. The next most pleasing interval is the octave. In the

1. Some scholars would prefer to define a chord as having at least
three different pitches, but this point is not important to the
pr^ent discussicm.

28 Pitch

3-3

octave, the frequency of the upper pitch is exactly twice that
of the lower pitch. Most musical scale systems are based on
the relatlonshfp of the octave. For example, the Arabs use an

octave divided into equal sixteenths, and the Hindus divide
the octave into twenty-two steps, but use only seven of these.

The Western system of music usually divides the octave into
twelve parts. In the early days of music, these divisions were
tuned in what is called just (as in "right") intonation. Although
the twelve divisions are unequal, the frequencies of these
pitches have very dose relations toeacho^r. Asan example,
the perfect fifth has a ratio of 3:2. In other words, If the
upper pitch is 300 Hz, then the lower pitch will be 200 Hz.
Fig. 3-1 shows the frequenby ratios of ^e Intervals in the |ust
tuned scale. It should be noted that the consonance or
dissonance of an interval Is closely related to the ratio of the
frequencies of that interval. The smaller the numbers used to
express the ratio, the more consonant the interval.

The scale of just intonation produces harmony which is
pleasing to the ear because of these interval relations, but it
causes major problems with instruments using fixed tuning
systems such as the piano or organ keyboard and guitar
frets, tt is impossible for this type of instrument to modulate
to distantly related keys without retuning the instrument

The linabtHtv to modulate freely was one of the reasons for

the development of what we call the scale of even (or equal)
temperament. In this scale, the octave is divided into twelve
agua/ parts. The frequency ratio between any two adjacent
notes (semitones) is exactly the same. With equally spaced
pitches it becomes obvious that the intervals in a scale
ratalti the tame mtadohshfp no matter which note Is used
for the starting point. The frequency ratio of a major sixth
will remain exactly the same no matter which pitch is used to
build it on. The unaqinil dNtlons of the Just scale will form
correct intervals only wrtien certain pitches are used as the
starting point.

Fig. 3-2 shows the frequency ratios for the scale of even
temperament. Fig. 3^ shows a comparison of the frequencies

between the scale systems using a one octave scale starting
on middle C. If we assign middle Cthe frequency of 264 Hz
(which It often is In setentific iaborsitoriei), the frequents
of the two scale systems would be as shown. Also note that
expressing the frequencies of the just scale accurately requires
fewer digits.

Beat Frequencies

AltfiouE^ Western music primarily uses the equally tempered
scale, the scale of just Intonation is not obsolete. The violin,
for example, has no frets and can, therefore, play intervals
of any frequency ratio. Most good violinists have a tendancy
to sound just intervals in whatever key they are playing>eii!en
when playing with inflexible evenly tempered instruments.

The reason for this is the interaction which takes place
u^en tira dcHdy related pitches are sounded together.
This interaction tikes the form of a wavering in the loudness

Fig. 3-1 Frequency Ratios for Scale of Just Intonation
(a) Interval RatftA

Interval

Frequency ratio
from starting point

Unison .,* 1:1 1

Semitone 16:15 1.066667

Minorlone 10:9 1.111111

Major tone 9:8 1.125

Minor third 6:5 1.2

Major third 5:4 1.25

Perfect fourth 4:3 1.333333

Augmented fourth . . . 45:32 1.40625

Diminished fifth 64:45 1.422222

Perfect fifth 3:2 1.5

Minor sixth 8:5 1.6

Major sixth 5:3 1.686667

Harmonic minor seventh .... 7:4 1.75

Grave minor seventh, 16:9 1.777778

Minor seventh 9:5 1.8

Major seventh.^ i . . ...... . . 16:8 1.875

Octave 2:1 2

Cents*
from start
point

111.731
182.404
203.910
315.641
386.314
498.045
590.224
609.777
701 .955
813.687
884.359
968.826
996.091
1,017.597
1,088.269
1,200.000

'(See p. 32)

(b) Intervals in Order from Consonance to Dissonance

liMHwtt iSHlon btt&«

Fraqumoy

2:1

3i2

Major
tIMh

S:3

U46r
thtrd

S:4

4:3

Minor
thtid

Minor
itxth

S:6

Fig. 3-2 Frequertcy Ratloe for Equally Tempered Scats

Frequency ratio
" ^"'^ from starting point

Unison 1:1

Semitone or minor second . 1.059463:1

Whole tone or major second 1 .1 22462:1

Minorthird 1.189207:1

Majorthird 1.259921:1

Perfect fourth 1 .334840 : 1

Augmeinid fourth » 1414214-1
DIminUhed fifth f"-f

Perfect fifth 1.498307:1

Minor sixth. . . . ^ , 1 .587401 : 1

Majortixth 1.681793:1

Minor seventh 1.781797:1

Major seventh 1.887749:1

Octave 2:1

Cents' from
starting point

0
100
200
300
400
SCO

600

700
800

900

1,000
1,100
1.2Q0
•(See p. 32)

Fig. 3-3 Comparison of Scale System Frequencies

Just o o o o o q

Intonation S R 9 f:i SS 2

Equal
Tempering

•5

>- CO

(0 n
w ci

Ul u. (9 < m u

of the total sound and is called a beat. Fig. 3-4 illustrates
this. For simplicity, 6 Hz and 5 Hz are shown rather than
audio frequend«n. Vt^ve^nti (c) mipresents the algebraic
addition of waveforms (a) and (b). The changes in loudness
can be seen clearly in (c) where the sound starts at maximum
Idudn^, dies dbwh t& minimunri at the center of #i« #ar
gram, then expands again to maximum loudness jfftlJWHld of
the period shown. In other words, the frequency iatf liie
loudness variations is one cycle per secomi, at 1 Hz. Ndte
that 6 Hz — 5 Hz = 1 Hz. For near unison, then, the beat
frequency will be the difference between the two pitches.

Other intervals will also produce beats when they are mistuned.
The ease with which these beats can be heard wilt depend on
the consonance or dissonance of the interval; the more con-
sonant, the easier they are to hear.

As an example, if we start with a pitch of 440 Hz, a perfect
fiftfi above this would be 660 Hz because the frequency ratio

ofaperfect,fifthi83:2(-| = -||^). If t^p^r #itBh

happens to be 663 Hz, then we will hear a beat frequency of
3 Hz because the upper pitch Is 3 Hz higher than the cor-
rect 660 Hz.

In the equally tempered scale, the frequency of a perfect
fifth above 440 Hz is 659.26 Hz (see chart facing p. 66).
The result is that when an equally tempered fifth is sounded,
we hear a beat of 0:74 Hz (660 - 659.26 = 0.74). A good
violinist would have a tendancy to adjust his/her pitch to
eliminate this beat when playing harmony with other Instru-
ments.

Musical instruments are very often tuned using beat fre-
quencies. The instrument being tuned is first adjUlted so that
it produces a pitch at approximate unison (or some other
interval, if desired) with a reference such as another instru-
ment, a tuning fork, or a test oscillator. The instrument is
then sounded together with the test pitch and fine tuned to
eliminate ^e best

The presence of beat-producing intervals in the equally
tempered scale is a useful point to keep in mind when
working with electronic music. Many sounds in electronic
music are of a character which makes these beats easier to
hear than if the music were played on acoustic instruments;
therefore, it is sometimes necessary to compensate for this
by hiding tflese beats under the oversll musical texture, or
by employing some other means to correct offending pitches.

The Natural Harmonic Series

In Chalrter One it was shown how vibratory systems tend to
Ibe quite complex, vibrating at various frequencies at the
same time. These frequencies are called overtones. In most
systems, these overtones have definite mathematical relation-
ships with each other so the upper overtones are all multiples
of the lowest or fundamental. Overtones of this type are
harmonies.

Fifl. 34 frequency WavB^nfl

30 Pitch

If we design an open end pipe or a monochord which pro-
duces a fundamental at the pitch of A2 {bottom space bass
cleft), and If wd ucfi'^tt mcisleal notate^^^Bm tasNtw^»'
pitches of the possible harmoni^j th9 result up to the
sixteenth harmonic would be as stiolvn in Fig. 3-5. This
diagram gives a compartfbh of tfte actual fraquencies of the
harmonics in relation to the frequencies of the equivalent
pitches in both the scale of just Intonation and the equally
tempered scale. Note that the hamitinfes ihdwn as ^aattar
notes do not match the frequencies in either scale system.
Also note that except for these quarter notes, the pitches in
the scale of just intonatfon m&Ai tbe harmonics. And last,
that in the tempered scale, CHlly ^^..OE^ves of the funda-
mental {all the A's in this case) mate*i the harmonics. This
series of pitches is called lhe natural hannanlc s«1es.

FiB. 3^ Natural Harmonic Series for A2
A

gWt

0 <>

Nbttib of nets: A3

EiS

G«

0#«

A«

Nunttierof hamionio: 1

Frequency of

-0

true harmonic: 3

w
0

u
0

oi
0

•J
0

0
0

to
0

Actual frequencies of the notes shown:

Juit
intonation:

Equel

tempering:

o o

(Jl

00 to

S 8

b b

3-5 Consonance and Dissonance

With the preceding as background it is possible to give a
better understanding of what causes consonance and dis-
sonance in musical intervals. In Fig. 3-6 are shown some
pitches with some of their harmonics written above them.
The pitch in (b) is shown one octave above the root in (a).
Note that if these two pitches are sounded together, most of
the harmonics In (a) reinforce the first harmonics in (b).
"(^O'K that in (c), which shows the perfect fifth above the
root, fewer harmonics match. With the strong dissonance
of the minor second shown by {e), none of the harmonics
match. Also note that (a), (b), (c), and {d) form a major
triad and that when sounded toge^er many of the hannonrcs
coincide with each other.

Pitch 31

Fig. 3^ 6eniw>an^ipKl DkiatBrK»

® ROOT

(b) OCTAVE
(Consonant)

©THIRD

Harmonic number

@ MINOR SECOND
tDissonant)

Whole notes rapretent musical pitch; quartnr notes
nqsresem^ lowmr hamnonlcs of those pitthes.

3-6 Pitch Standard

Usually, the A above middle C is used as a standard for
designating the frequencies of the pitches in music. The pitch
of this A has changed over the years but most countries
today use A = 440 Hz. Throughout history, however, this
pitch has varied from about 373 Hz to about 462 Hz. As an
example, the A in Handel's time was 426.6 Hz.

3-7 Exponential Prograuiom

The relation between pitch and frequency is an important
one, especially from the point of view of electronic music.
If we start at the bottom df the piano and play a chromatic
scale all the way to the top of the keyboard, to our ears it
will sound as if all the pitches move upward in evenly spaced
steps. For example, ihe distance between e C end a D et the
bottom of the keyboard and at the top of the keyboard will
sound the same because the ratios between the frequencies
are the same. The frequeneies themselves, however, are quite
different. The difference between the lowest C and D is about
4 Hz. The difference between the highest C and D is about
256 Hz.

If we start at the bottom of the keyboard and ptay all the

A's movfr^ tilW^ntlt, the distance between each pair of A's
remains musiieally ttie same (one octave), but the frequency
doubles with ead) A. This kiN of progression is called an
exponentid progression.

In measuring things we usually use a linear scale In which
the divisions are equally spaced. The divisions on our rulers
are equally spaced. A centimetar on one end is just » long as

a centimeter on the other end. The compass has 360 equally
spaced degrees. A day has twenty-four evenly spaced hours.

With some things it is more convenient and practical to use
an ncponential sc^le. The ^}de rule is a good «eampie.

The divisions of most of its scales are unequally spaced; a
measure of one unit is longer on the left end than it is on

the right end. Moving from left to ri^, the difftartees^r otie

unit become progressively shorter.

Fig. 3-7 shows a comparison between a linear scale and an
exfKmential scale. The upper divis1or» repre^m oetave
intervals. Frequencies are shown below this and result in
an exponential scale, a scale in which the divisions become
pra^«5Slwly smaller towards the right. Most graphs which
deal with sound use an exponential scale to show frequencies
because this has a "linear" sound to our ears.

Fig.3-7 Pitch/Frequency Comparison
PITCH (linear prosression):

Ai
—i—

-Middle C

FREOU£NCV toqWiMntial prograMfon):

H — I 1 r I I I
9 S S^SSS

t ' r 1 I I i

H — I — I — 1 I I n

O O OOOOOQ
O O OOOOQQ
O O OOOOOO

Cents

In the above, the differences between the frequencies of the
pitches of a mfrfor ^MM>hd at the top of the kieyboard and at
the bottom of the keyboard show that the use of frequency
for the measure of the accuracy of pitches is inconvenient.
For this we use the cent. The cent is based on the equally
tempered scale with 1200 cents equal to one octave. This
means tfiat a minor second is 100 cents. In experiments it
has been shovm tfiat when two independent pftches ate
sounded one after the other for comparison, the average
person can detect a difference of pitch as small as about
three cents.

Voltage to- Frequency Relations

From the above, it can be shown that there are two possible
practical approaches to establishir^ fttlationshlp betwran
the amount of control voltage change needed to produce a

given VCO pitch change.

The first of these systems uses what is known as a linear
VCO. Ih ^tk type VdO, the ft^sqaeney output of the VCO

is directly proportional to the control voltage applied. For
example, such a VCO might have the following vottage-to-
frequency r^atlons:

control VCO
voltage frequency
input output

1 volt = 110 Hz (A2)

2 = 220 (A3)

3 = 330 (approximately E4I

4 = 440 (A4»
etc.

Unfiar
prf^Sitsion

Ejqionential

Or, to produce ^e octaves only:

Pitch 33

Exponential

voltage

progi^on

control VCO
voltage frequency
input output

1 volt = llOHzfAz)

2 * ^ (A3)
4 - 440 (A4)
8 » 880 (A5)

etc.

Linear
pitch

progression

Linear
voltage
progression

Linear
pitch

progression

To produce a series of octaves moving upwards, therefore,
requires a control voltage source which incressss In exponen-
tial steps.

The second approach uses what is known as an exponential
VCO. In this type VCO, the pitch output of the
VCO is directly proportional to the control voltags apidied.
For example, such a VCO might have the following voltage-
to-frequency relations:

VCO
frequency
output

110 Hz (A2l
220 (A3)
440 (A4)
880 (As) ,
etc.

In this system. It is neeessary to provide linear changes In
voltage to produce a progression of octaves.

3^10 TheUnearVCO

Fig. 3-8 (a) shows a plot of the voltage-to-frequency rdations

in the linear VCO of the example in 3-9 above. From this it
can be seen where the term "linear" originates. In (b) is
shown the plot for the voltage-to-^tdh [relations for the same
VCO. The resulting plot forms an exponential curve. To
produce any even progression of pitches, such as octaves
(as shown) or a chromatic scale, would require exponential
changes in the control voltage source. This fact produces
problems in connection with tuning and transposing. If we
have a voltage source which produces an exponential sequence
of voltages, as for example: 1v*, 2v, 4v, 8v, and feed this
sequence to the linear VCO of this example, it will produce
pitches which make one octave jumps starting at 1 10 Hz A2
and ending on 880 Hz As, as shown in (b). To raise this pitch
sequence one octave so that it starts on 220 Hz A3 and ends
on 1760 Hz would require that we double (multiply by
2) the Input control voltage. The linear VCO, then, needs the
addition of an electronic multiplier at its input if it is to be
able to transpose freely. It also requires an exponential
keyboard, or a keyboard which produces voltage steps which
increase exponentially when a chromatic scale is played.
Since the keyboard control voltage is often used for other
synthesiser control functions, other system parameters
woufd also have to be deigned to ttitfteh Ihis exponential
relation.

3-1 1 The Exponential VCO

Fig. 3^ fa) $hows a plotof thevottage-to frequency retadon
in tfie exponential VCO. The main different between tiiis

•tv = volt)

Fig. 34 UnsarVCO

® Voltage/Frequency ItoteSoni

200 400 600 800 IOOO
Frequency

(b) Voltage/Pitch Relation

34 Pach

curve and the one shown in Fig, 3-8 (b) is that it moves up
and turns right instead of moving right and turning up. Fig.
3-9 (b) shows the voltage-t<H)itch relation In ^ exponential
VCO. From this it can be seen that the names which are
applied to these two types of VCO depend merely on point
df view. The exponential VCO produces a linear voltage-to-
pitch relation and the linear VCO produces an exponential
voltage-to-pitch relation. Electrical engineers are usually
more concerned with oscillator frequency relations than with
musical pitch relations, and it should be remembered that
VCO's are used in other areas of electronics and not just as
pitch sources for synthesizers. The names applied to VCO's
are from the point of view of frequency.

In music, since we are usually more concerned with pitch
relations than frequency relations, the use of exponential
VCO's where pitch is directly related to control voltage might
seem the more logical choice for synthesizer pitch generation.
Any linear source may be used to produce accurate musical
scales^ and linear voltage sources are easier to match to other
system parameters. Transposing and tuning become extremely
simple, merely the mathematical addition of voltage sources.
To transpose or tune an exponential VCO it is necessary only
to supply a fixed voltage of the proper level in addition to
the pitch control voltage.

Slnea the exponential VCO uses Hnear inputs to produce
exponential changes in frequency, it requires a linear-to-
exponential converter. This exponential generator, as it is

called, is an integral part of all exponential VCO's. Elec-
tronically, exponential generatoi^ are not too difficult to
design. The major difficulty is thattiiey are quite temperature
sensitive, in earlier exponential VCO's, this dependency on
temperature changes meant that the VCO's had to be con-
tinually retuned since they would quickly drift off pitch.
Temperature compensation used in modern VCO's, however,
produces pitches vtrhidi are very stable.

The exponential VCO is the most common VCO in use in
voltage controlled synthesizers today. The most common
voltage-to-pitch standard In use (s 1v/8raH volt per octave),
as shown in the previous examples. This means that if the
control voltage input is changed by one volt, the VCO
pitch will change by one octave. To produce a pitch change
of a semi tone would require a 1/12 volt change in control
voltage since there are twelve semi-tones In one octave. The
relationshTp of Iv/Bva Is qrulte convenTent. ft prababty eame
about as the result of the design requirements of synthesizer
circuits. With the most common power supply voltages used
In many circuits eorrtaining IG^ Ontsgrated efreuift},, la
relatively simple to obtain variations in^ol^^ Whl^mtiain
perfectiy linear between 0 and apprOidmattety +12 volts.
Witii- a ^^nstaid of 1v/8va and using +10 volts as an ap-
prcxicYfni^' iUpper limit will produce a pitch range of ten
octaves vt^tchi eovers all audible frequencies. If we specify a
voltage ae^iracY of ^iO. millivolts (tCM)1 voltK tills will

Fig. 3^10 shows tiie block diagram for a typical exponential

Fig,3^ Ea^onatitte) VCO

0 Voltaea^re^itieney Flelation

Pitch 35

voltage controlled oscillator. At the bottom of the diagram
are three control voltage (CV) inputs. The KEY CV (from
the keyboard) has an ONASFf= switch so that, if desired, the
VCO frequency output will have tlo relation to the keyboard.
The VCO in this example provides two other control voltage
inpan, both VS^ voTuhie controls so that the input may be
attenuated (reduced). The VCO TUNING control is nothing
more than a variable voltage source Inside the VCO. The
summing ampliffef does exactly wfhat the name implies: it
adds all the control voltage inputs together to produce one
voltage level to produce the desired VCO pitch. For example,
if the teuF eotmol iroHage inputs were +1.50v, -0.82v,
+1.32v, and %0Ov rwpectively, the sum would be: +2.00v.

Fig. 3-10 VCO Block Diagram

EXPONENTIAL
VOLTAGE
CONTROLLED
OSCILLATOR

Exponential

Voltage

Controlled

Osdltator

Modulation

Deptli

Contreto

OUT

A A

Key CV CV
CV m IN
IN

•NOTE : Many VCO's do not prMde tine wave shapers since
tbi^maa is^emlfy produced by filtsring the
tifan^ wave.

36 Pitch

This voltage might produce the piteh of mtiE^e C, as an
example. The actual pitch wilt depend on the design of the
VCO but the standard used is not too Important because we
are usually more eoti^ed >ui#i ^eresultins pMtNut tfw
aefefit ifttemel voltw rwcass«v 10 pfoduds mt piteh.

After the summing amplifier is the exponential converter
which converts linear changes of voltage input Into the
exponmttal changes wAtdi control the oscillator Itself. The
most common form of oscillator is a type which generates a
sawtooth wave; if other waveforms are desired, wave shaping
drcuite must be Incorporated at the output as ^own In tiie
diagram.

The Low Frequency Oscttlator

A low frequency oscillator or LFO is an oscillator which
produces low frequencies usually starting from somewhere
just above the lowest audio frequency (25 Hz or 30 Hz, for
example) to frequencies far below the range of hearing. A
typical LFO might reach as low as 0.01 Hz, which requires
ten seconds to prfiduce one complete cycle. In some systems,
VCO's can be used as LFO's, but most systems also provide one
or more oscillators which specialize in generating low fre-
quencies. In large systems, even the LFO's are voltaQe con-
trollable with a voltage-to-frequency relation the same as the
system's VCO's. Also, like VCO's, the LFO often produces
several Wav&forms, the most common being the sine wave.
If a low frequency sine wave is applied to a VCO control
voltage input (Fig. 3-1 1 ), the result will be a wavering of the
VCO frequency (pitch) at the UrO rtfte. This produces an
effect whi^ in music is called vibrMp.

Frequency Modulation

Modulation teftirs to di« control of one parameter by 9nq#)^,

the basic conc^^ Of the voltage controlled synllwslaser.
Controlling the Trtquancy output by means of an «(tsmal
control is a fomn of fteflKiency modiilirtiion (FM). Both

vibrato and pitch control are forms of frequency modulation.
Fig. 3-12 shows the waveforms obtained with LFO control of
thff Vt!0. In (to) is shown *e VCO output vrithout modula-
tion. In (c), (d), and (e) are shown the VCO output with
various depths of modulation. The + and — excursions of the
LFO viravefoitn in (a1 cause t^speetTva fnoreaMS and decreases
in the frequency output of the VCO waveform. The deeper
the modulation, the farther up and down the VCO frequency
sweeps. The average frequency, or We frequency in the
center of the VCO sweeps, is the same as the frequency
would be without LFO modulation.

Fig. 3-13 shows a block diagram for FM radio broadcasting
which works on exactly tiie same prindpal.

The Basic Synthesizer Patch

Fig. 3-14 shows the basic synthesizer patch with the addition
of VO^ modulate imm- VGO dBmrit^ m waveform
continuously, *e frequency of tfie waveform depending on

Hfl..3t-11 LFO Modulation df VG0

VCO

Pitch
control

LFO

OUT

Fig. 3.12 Frequency Modulation WaVBftmni

(a) LFO Waveform:
(Modulating wave)

@ VCO Sine Wave
without modulation
(carrier)

Modulaud VCjO wamfemis

® Medium:
(Exaggerated
vibrato)

(e) Deep:
(Special
effects)

Pitch 37

the sum of the control inputs. The next chapter shovw how
to start and stop the sound in order to produce separate
musical notes.

FiB4 3-13 Prequmey Modulation

FM RADIO

RF Carrier

In m

Oscillator

Modulator

RF ■ Radio frequency

Audio
frequency'

Audio
inputs '

Audio
Amp

Antenna

Modui«t«ef'M»iMW

Transminer

38 Pitch

3-15 Questions

1 . What is the diffei^ice l»tween the scale of just intonation and the equally tempered scale?
2i What Is a beatftequency? Describe how an instrument is tuned using beat frequencies.

3. What is ^e natural harmonic series? What are tiie musical pitehes of the first harmonics for middle C?

4. Explain what cau^ consonance or dissonance in a musical interval.

5. What is an exponential pq^osPBSSidn?

6. Explain the vdltage-to-frequency/g^|(^ rdation in a linear VCO.

7. Explain the vbltage-to-frequency/pHsh relation in an exponential VCO,

8. What is a low frequency oscillator?

9. What is frequency modulation?
10. What is vibrato?

Words to define:

beat frequency
cent

even temperament
exponential
exponential generator
exponential progression
exponential VCO
FM

frequency modulation

just intonation

LFO

linear

linear VCO

low fi^quemsy otdlla^or

modulation

natural harmonic series
VCO

vibrato

voltage controlled oscillator

Loudness

Chapter Four

■1 Introduction

The first thing that comes to mind concerning loudness
is perhaps dynamics (changes in loudness) in music, so
loudness might seem less important than the other two quali-
ties of sound. The envelope of a sound might also seem to be
of not too great importance when trying to indentify a sound
source, but this is not so. The effect of the envelope on a
sound is so great that in approaching the synthesis of a sound,
it is usually far better to synthesize the envelope Isefore
ccmslderins tone color.

Before considering loudness as a quality of sound, however,
we should first discuss how loudness is measured,

2 MSaiurihg Loudneu

One way to measure loudness is to measure the pressure
changes which take place in the air as a result of sound waves.
Atmospheric pressure is usually measured in units called the
bar. One bar equals normal atmospheric pressure at sea
level; or about 70 kilograms per square centimeter (14.7
pounds per square inch). Since air pressure changes caused by
even the loudest sounds are too small to be measured with
a unit as large as the bar, we use the microbar (often written
Mbar; 1 ijbw = 0.000001 bar).

Another unit used to measure sound level (among other

things) is the decibel (abbreviated dB), named after Alexander
Graham Bell (1847-1922). Most of the confusion associated
the dedbel Is #ie fesuk of the fact that it is not in
itself a measure of level and therefore, by itself, is meaningless.
(Another point of confusion arises from the fact that the
decibel scale is exponential, rm linear). The decibel is a
comparison between, or a ratio of two quantities, in this case,
loudness. If we hear two sounds of different intensities,
it is possible t& mM6{m thm Bn^ smi that the first Is 6dB
(for example) louder than the second. At this point we do
not know how loud either sound is, just that one is a specific
amount louder than the o^er.

To me ^e decibel as a unit of sound level measure, we must

first establish some reference level for comparison; then we
can say that a given sound is a certain amount above or
below this reference.

For acoustic research, aft aneohole chamber is used. This is a

specially built room with all the walls heavily insulated to
keep out as much external sound as possible. The interior
is designed so that all sounds made within the room are
absorbed as much as possible to eliminate reverberation.
Besides acoustic research, these rooms are often used by
manufacturers of microphones and speakers to test amf rate
their products.

Using an anechoic chamber, it has been determined that for
the average person the threshold of hearing, or the point at
which sound just becomes perceptible, is 0.0002 i^bar. The
opposite end of pur hearing range is the threshold of pain,
or the point where sound starts to be perceived as feeling
(pain). The tiireshold of pain was found to be about 1,000
/xbars.

40 Loudness

Sound pressure level (abbreviated SPL} is a decibel scale which
uses the 0.0002 ixbar threshold of hearing level as a zero
reference point The tiire^old of hearing, then, is 048^ I^L

Fig. 4-1 shows the sound pressure levels of somft ieCKtmnon
sounds. Note particularly the relation betweftn ■flSe SPL
scale and the ;ibar scale, and compare this to "tfie relation
between pitch and frequfeney (Fig^ 3^7). If we insert a test
signal into a hi-fi amplifier which is capable of producing
very loud sound, and if we start with the volume control at
"0" and turn It up at a steady rate of speed in steps of about
3dB each, to our ears the loudness of the sound will seem to
increase in steady even steps, much in^e same way as pitch
increases in a chromatic scale. And like frequMiey, the air
pressure changes in jubarS will incTvase exponentially.

Fig. 4-1 Relative Loudness Levels of Common Sounds.

m = meter I

Average factory-
Average automobile —
Convenation (1ml — i
Average office — |

Quiet residential street-
Average home-

VBry toftmuslc 1

Quiet whi sper [2m)

An echoic chamber

I l l ll llll — I t 1 1 I I I

44-

I I HIM

Bus interior
1 — Heavy street traffic (2m)

I — Heavy truck (35m)

factory

■Hammering on steel plate (.75m)
I — Pneurnatic chipper (2m|

Threshold of pain

50-hp siren (40m)

-HW4

0.0002

0.002

0.02

0.2

200

nnnn Sound pressure

0 10 20 30 40 50 60 70 80 90 1 00 110 1 20 130 1 40 DECIBE LS

llll|fi n jlfl MHI l[l M I| M tlj n il M llll n ilh MH l u t MHM [lll.llt M l|llll|II N j LlM I M

I 1

fTftt

—Be

ickground music

I — Mmimum street noise
I I

' — Very quiet radio at home

' Country houis

-Quiet auditorium
' — Quiet sound studio

Leaves rustling
— Thrfishold of hearing

Loud mutic (rock]
Thunder
I — Passing subway

' Riveting machine (15m) or vary loud music (claislcal)

' — 10-hp outboard motor (20m)
lJ6udnfuir6{cbisfeal)
' — Heavy traffic {10-20m)
' — Department store or noisy office

The smallest perceptible change in sound level which the
average person can detect is roughly 3dB but this will
depend on the overall level and the frequencies involved.
In other words. If we produce two separate sounds of the
same pitch one after the other, they would hwe to ^
proximately 3dB different In intensity before iS)e levels
would seem different.

4-3 Frsquency ResponsA of the Ear

The ear is more sensitive to some frequencies than others.
This sensitivity is also strongly dependent on the loudness
of the sound. This is shown in Fig. 4-2. The llift margin 0f
the graph shows sound intensity in dB SPL. Intensity refers
to the level of sound as measured with instruments. The
curves on ihe gr^apAi show kiucbietB, whidi i^Xers to the
subjecti^ level of sound as perceived by tfte ear. Both

loudness and intensity are measured in dmmt but to

c^^de at all l«quencfes. the term phon is often used to
measure loudness.

Tl °' '^^^^^^ ^''^ ^ short firt spot

at the ],000 Hz point. This is why 1,000 Hz is used as a
reference point in these curves (and why recording studios
often use 1 ,000 Hz as a test frequency or a level reference in
equipment). In other words, for a frequency of 1,000 Hz the
oudness level in phons Is exactly the same as the intensity
eve! m dB SPL. These curves can be taught Of « shovrtng
the intensity levels which would be necessary to give all
frequencies the same apparent loudness as the 1 QOO Hz
reference frequency. For example, to make a 100 Hz pitch
sound as if it has the same intensity as a 50dB SPL 1 000 Hz
pitch would mt>W9 an Intensity level of about 68dB SPL
Ithe^BO phon curve crosses 100 Ht line at about .6808:

The bottom-most curve on the graph, the 0 phon loudness
curve, represents the threshold of hearing for various fre-
quencies. At 1 ,000 Hz. the threshold of hearing is OdB SPL
Lower frequencies, however, require higher intensities before'
they start to b» hearti: l^of example. 100 Hz requires a
level of 38dB SPL before it starts to be heard, while a fre-
quency of 30 Hz requires an intensity of more than 60dB
bKL. From this itcan be seen why soft bass passages will cause
a tape recorder VU meter to jump higher than treble passages
of the same apparent loudness.

These curves, of course, represent average values. They would
ook slightly different fof diffemnt people and slightly dif-
ferent for the left and right ears. This would perhaps explain
why people like different settings of amplifier tone controls
One might wonder at a friend who likes to turn the treble
o^rol up too high; it could be because his/her hearing is

Another point in connection with these curves is that most
knobs which control level in electronic equipment control
the mtensity rather than the loudness. Thus, it is quite pos-
sible to set a control low enough that the lower frequencies
are below the threshold 6f heaHng. Some hi-fi amplifiers
have a "loudness" control which theoretically can be set at
any point and still retain the same apparent loudness for all
frequencies So that with low listening levels they are not

Since the loudness of different frequencies varies with the
setting of the system level controls, it can be seen that it
would be extremely importfintduringthe process of recorifing
electronic music to monitor the output at the same level at
which the finished recording is expected to be played.

Dynamic Range

The dynamic range of orchestral music can exceed lOOdB In
0^ wo^ if we call the level of the softest passage
uau. the loudest passages can ex(»ed +100dB. Hectronic

42 Loudness

recording and reproduction equipment can seldom match
this performance. The upper limit in such equipment Is
dtftefmined by the level of signal which can be processed

before distortion occurs. The lower limit is determined by
the noise level of the equipment. All electronic equipment
generates a certain amount of noise. This noise can be heard

as a hissing sound when the system volume controls are turned
up high when the system is not processing an audio signal.

The usable dynamic rangie of an ordinary good quality open
reel tape recorder is on tfte order of about 5& to 60dB.

This, of course, Is it0iii^iQYe;;(i6ar the lOOdB dynamic ran^ of
live music. A little analysis will show that this is not; bad
as it seems. If we assume an average home with a backgfdund
noise level of about 45dB SPL {Fig. 4-1), it would be neces-
sary for the music level to be either the same or more than
this for It to be heard. Any lower level would be masked or
covered by the background noise. If we add a lOOdB dynamic
range to this 45dB SPL background noise, we get a top level
of 145dB SPL for the loudest passages in the musfc. Ignoring
the effect this would have on neighbors, this level is well
above the threshold of painl Assuming a conservative dynamic
range of dfobut SOdSfbr a fape r«cor3frig, the liDudest passages
would reach a level of 95dB SPL, a little more realistic level
if the listener likes very loud music and has understanding

Fig. 4*3 shows two audio waveforms. In (a), the input level

of the signal has been adjusted so that the peaks are just
inside the maximum permissable level of the equipment
processing the signdi. Tlw dotted line shows the average level
which represents its apparent loudness. In (b), even with the
peaks going over the maximum permissable level (thus
distorting tha sl£piai)r the sv«r^ level and the apparent
loudness is lower than that of (a).

Fig. 4-3 Relative Sound Levels

Maximum

permissible

level

Approximate

® will sound louder than (£) even though thepMlcs titf ®
are much higher then those of (|).

4-5 Intensity of Harmonics

The tone color of a sound' source Is determined by the

number of harmonics contained in the sound and their
relative intensities. This is another aspect of loudness as a
quality of sound. The importance of the Intensity of the
harmonics in a sound can be demonstrated by examining the
harmonic content of two waveform* opmmonly used in
sy nthesii : ^ square warn and the ^tangle vMve. The speetnim
diagram for the square wave is repeated in Fig. 4-4 for easy
comparison with the spffmim diagram of the triangle wave.
Note that, ffitccept for the intensity of the harmonies, these
waveforms contain the same harmonics: all the odd num-
bered harmonics. In the case of the triangle wave, the
intensliy df the «)dst!ng harmonics is so tow tiut the triangle
wave has a tone quality very near that of the sine wave; a
tone quality very far from that of the square wave. In Chapter
i it will he shown how the square vrave can be Mterad so
ihat it very closely approaches the shape of ^e iblangle wave.

Loudness 43

Fig. -M SYNTHESIZERWAVEFORMS

HARMONIC SPECTRUM
OF PERFECT SQUARE

WAVE

-10
-20

— .tn

-40

-50

HARMONIC

FREQUENCY

6X 7X

11X

ISX

AMPLITUDE

A/3

A/7

A/9

A/1 1

"■ A/18

-9.5

■17

-19

-21

Note that the denominators of tiie 9rnp|;tude fractioni above ars the same as the harmonic number.

HARMON IC SPECTRUM
OF PERFECT TRIANGULAR
WAV6

-10

-20

dB -30

-40

-50
-60

HARMONrC

13 15 17

FREQUENCY

5X 7X

tlx

13X 15X 17X I9X

AMPLITUDE

A/a

A/2S A/49

A/81

A/121 A/iraA/22Sll/a9Aj3It

-19

-42

45 -

47 -49 -51

Note that tiie denonrinttOfS^^ aM^ucifrlrsc^ the s

H Of the iian$toiiii& humtiigr .

44 Loudness

4^ Envelopes

The voltage controlled amplifier or VCA is the primary source
of level control during the production of notes on the
syntherizer* The term "amplifiiw" might actually be con-
sidered a misnomer since in many synthesizers the normal
output level of the VCA never exceeds the input level. The
important point, however, is that the output leva! ts ^trolled
by an externally applied control voltage.

The shaping of the loudness contour or envelope of a sound
is done by controlling the VCA with an emrelope gen-
erator (sometimes called an ADSR, named after its
controls^ or sometimes called a transient generator). The
output of the envelope generator Is a cmtrd iKittageWhii^.
when applied to the control input of the VCA, gives the
sound its loudness contour.

When a key on a piano is struck and held down, the resulting
envelope will be (ike that shown in Fig. 4-5 (a). Th^ thtie
required for the sound to jump up to maximum is called
attack time. The time required for the sound to die away is
called decay time. If the piano key is released before the
sound has had a chance to die away completely, the sound
will be quickly dampened, as shown in (b). This is called
release time.

Fig. 4-6 shows two envelopes possible on modern electronic
organs. In (a) is shown an envelope possible only on electronic
instruments. As shown, attack and release tlm^ are 2ero, an
impossibility. In actual practice, these are probably on the
order of a few milliseconds or so (1 millisecond = 0.001
second). The very fast attack and decay cause this envelope
to produce a very artifical electronic sound; such sounds
normally do not exist in nature. In (b) is shown an envelope
with slightly longer attack and rel&as^ times used to fmit&te
the start and stop of the air flow through an organ pijse. Both
these envelopes introduce the element of sustain since the
sound will continue as long as the related key Is held down.
Notice tiiat in botii (a) and (b), decay is missing.

Fig, 4-7 shows a synthesizer envelope which contains all
four elements of the envelope: attack (A), decay (D). sustain
(S), and reiease (R). Pressing a key on the keyboard produces
a gate pulse which triggers the beginning of attack time 50
that the level of the VCA output sound begins to rise. When
the sdund reaches its-maxfrntmi Idvel ift ^6 end tif attack
time, decay starts and the sound falls to the level determined
by the sustain control setting. This level is then maintained
until the key is releioed. 'Releasing the feeV ojts off ^e gate
pulse and triggers the beginning of release time where the
sound finally dies away completely. Note that if the sustain
cdiml ^«Btstimimum, as wh^ aymhesizing tfte envelopes
jthown in Fig. 4-6 (v) and (b), the decay element is missing
and the decay corrQ^ol has no effect. The envelope shown in
Fig. 4-7 might be used for synthe^^riit brass irmjment
sounds, or any instrument in which aiji%p peraisu've playing
style is desired.

Fig. 4-8 the envelope generator output When synthe-

FiB. 46 Pianipf irmlllCMft
(a) Piano envelape

PtarioehmloiSa fdampariodi
Key
struck

A" Attack time
D - daisy ^nio
R " Release time

Fig. 4-€ Organ Envelopes

® Electronic
Key

Key
OFF

(St Pii»4>rsen
tCay
ON

-R - "0"

S " Sustain levei

sizing piano-like envelopes. Note the differences between
these and the envelopes shown in Fig. 4-5. The curves formed
by tile synthesizer envelopes are exponential curves. Experi-
ments have show/n that exponential attack, decay, and
release curves sound natural and that trying to generate
small fluctuations encountered In natural sounds ssmns to
add nothing useful to the sound as perceived by the ear.

VGA Control Response

One frnportant corttideration about the VGA Is Its response

fn relation to the input control voltage. In most VGA's, the
response is linear; a change of one volt in control voltage will
cause (Hie volt change tn 0w output signal leveL Kg. 4-0
shows the control response for a given VGA with linear
response. For example, if the control input is 2v, the output
Will also b6 2v. In (bh the output waveform is a faithful
reproduction of the loudnea contour at the control voltage
input.

Fig. 4-8 VCACbmiDl Response
0 Unear Response 14

Oitput
voltage

(§) Waveforms

Audio
OUT

Exponential

deesy

lOv 1

-A

-* ft-j

Some synthesizers give the option of being able to select
between linear and exponential response. Fig. 4-10 shows the
output of a given VGA wtth exponential response. Mote
that in {a), the output level is shown in decibels so the
graph forms a straight line. The response is exponential
because dedbel scale Is exponential For comparison, (b)
shows the voltage outputs for the same VGA. In this the
exponential response can easily be seen. As an example. If
the GOntrdt Input is 6v, the output vvlll 'be -40dB ss shown
in (a),or0.1v, as shown in (b). In (c) is shown the waif^Otms.
The signal and control inputs are the same as those ^own in
Pfd- 4-9 ib), but notft ^e marlced difference in the output
waveform. The control input represents the exponential
decay of an envelope generator. The output in Fig. 4-9 (b)
is a faithful copy of this expPnanttiif decay. Due to ^e
exponential response of the VGA in Fig. 4- 10, the exponential
decay of the control input produces a very exaggerated decay
iln itNt^i)Etpit|.s«t J&l^lilils is very useful for symfiestzing
^arp, percussive sounds.

Fftf. 4-10 VCA Control Response

® Exponential Response (dB Output) (g) Exponential Response (Voltage Output)

Control voltage (V) Control input

Q Waveforms

I I apEWda^ws "0" in the ou^t

A '

Loudness 47

4-8

Amplitude Modulation

Using the VGA to control the level of a source signal is a
-brm of ampittudfr mixiiMoii (AM), the same principal as

Fig. 4-1 1 Amplitude Modulation

RF Carrier

Oscillator

RF • Radio frequsney

Modulator

Modulated Carrier
Audio \

1' w %w

Antenna

Transmitter

Audio
inputs

Audio

frequency

Audio

Amp

4-9

is used In AM radio broadcasting (see Fig. 4-11). In music, a
regular wavering of sound level is called tremolo. This type of
amplitude modulation can be demonstrated by using an LFO
as the control input to a VGA, as shown in Fig. 4-12. Since
with no control i nput to the VGA, the VGA remains "closed",
It is necessary to supply a fixed voltage to the modulation
input so the output level remains at half Its normal
maximum level. In this way, the VGA will react to both
upward swings {+) and downward swings {— ) of the LFO
wnveform. The upward swings will cause the VGA to "open"
more and the downward swings will cause the VGA to "close"
more. Most VGA's provide what Is called an initial gain
control (or sometimes hold control) which can be used to
hold the VGA in a partially "open" condition.

Fig. 4-13 shows the waveforms' produced by the above
an^ngement. In (b) Is shown the VGA output with no LFO
modulation but with a fixed voltage (or initial gain control)
holding the VGA partially "open". In (c), (d), and (e) can
be seen how varfous depths of LFO modulation cause the
VGA output level to periodically waver above and below tfie
level set by the fixed voltage input.

The Basic Synthesizer Patch

Fig. 4-14 shows the basic synthesizer patch with the addition
of VGA modulation by means of the envelope generator.

A voltage appears at the keyboard gate output anytime a
key fs deptmed. Since this Voltage goes m and off with the
pressing of keys, it is called a gate pulse. The gate pulse is
most often used to trigger the envelope generator into opera-
tion. The ou^t of ^e envetope genen^r #ten "opens"
^e VGA to let sound out of the synthesi^r.

The next chapter deals with ihe control of tone color in the

output sound.

Fig. 4-12 LFO Modulation of VCA
I 1

— H VCF h

VGO

L I

Fixed
voltage
source -
(See text)

OUT

LFO

Fig. 4-13 Amplitude Modulation Waveforms
(a) LFO waveform

® VCA output
without LFO
modulation (carrier)

Modulated wavefomn:

(£) Shallow:
(Tremolo)

@ Medium:
(Exaggerated
tremolo)

(e) Deep:
(Special
affects)

48 Loudness

Fig. 4^14 The Basic Synthesizer Patch

( — ^-1

I LFO I '

1 I
I I

Key
CV

vco

VCF

Envelope ^**~\^

Kevboard
gate

pulse

_rL

II!!

Ill |i

i| III!

Ill

4-10 Questions

1. How is loudness measunsd?

2. When recording eiectrontc music, why is it importffit to monitor the music at the samfe level at which the

finished recording is expected to be played?

3. What limits the dynamic range possible in a given piece of electronic equipment such as a tape recorder?

4. What harmonics are contained in the square wave? In the triangle wave? What is the difference in harmonic
content between the two?

5. Draw the envelope produced by striking and releasing a piano key. Draw the envelope produced by a pipe
organ nou. Name the parts.

8. }f the sustain control of an envelope generator is set at maximum, what effect will the decay ccmtrol have?
Why?

7. Show the output waveform of a linear VGA wilh a sine wave input controlled by a piano-tike envelope.
Show the output of an exponential VGA under the same conditions.

8. What is amplitude modulation?

9. What is tremolo?

1 0. Draw a diagram of the basic synthesizer patch and explain how it worlcs.

Words to define:

ADSR

amplitude modulation
attack time tA>

dB SPL
decay time (D)

decibel
envelope

exponential decay

exponential VGA
gate pulse

intensity (of sotHid)

linear VGA
loudness
mierobaf ifi\>6t\

phon

release time (R)
sound pressure level

SPL

sustain (S)
^reshold eif hearing

tremolo
triangle wave
VGA

voltage controlled amplifier

Introduction

Timbre or tone color is that quality of sound which allows
us td distinguish between two sound sources producing
sustained sounds at the same pitch. Tone color is usually
very much affected by the pitch range and the loudness
contour (envelope) of the sound* so It is u»»lty better to
consider tone color last when synthesldrtg sounds.

Noise

All electrdnie eltmiHS deiiei^tteittitifi emounf c»f noUe^

in most cases tflfe notse is undesirable. In electronic music,
however, noise Ofl^n forms the starting point for tone color
in the syntiiMlis of ntm^pIMied sounds or fbr n^^t^ed

elements In sounds. In electronic music we are concenred
with two types of noise: white noise and pink noise.

Like white light, which is a combination of equal amounts
of all colors, white ncrfse fs a cdmbination of equal amounts

of all audio frequencies and produces a hissing sound. A
review of Fig. 3-7 will show that the number of separate
frequencies contained in eai^ octave Is doi^e the number
contained in the next lower octave. For example, the octave
between Aj (110 Hz) and A3 (220 Hz) contains 1 10 separate
frequencies (excluding fractions) the next higher oetatve^As
(220 Hz) to A4 (440 Hz), contains twice as many frequencies:
220. Each successive octave, then, contains twice the number
of frequencies as ^fr ne9Ct tower octave. A doubling 'crf
frequencies for each octave means a power increase of
3 decibels per octave. Since there are more of the higher
frequencies, these frequencies dominate the sound to give it
its characteristic hissing sound. This is aided by the fact that
the ear is less sensitive to lower frequencies.

Pink noise is noise which contains equal amounts of energy
in each octave. Since each octave (rather than each frequenoy)
is equal in energy, this type of noise sounds, to our ears, as
if it has an equal amount of all frequencies and produces a
rushing sound much Mice a waterfall.

Filters

The major source of tone color in the voltage controlled
synthesizer is the VCO for pitched sounds and the noise
generator for non-pitched sounds. The major source of
control over tone color changes are the filters, the most
common of which is the voltage controlled filter or VCF.

In Chapter One It was shown how a pipe or tube is resonant
at various frequencies. The fact that this is so makes the tube
a form of acoustical filter. If we speak into the end of a tube,
the quality of the voice emerging from the other end will be
quite different. The human voice contains a great many
different frequencies. When one or more of these frequencies
coincide with any of the resonances of the tube, these
frequencies are accented in the output sound in exactly the
same way as the sound of a tuning fork will be accented
when its frequency matches any of the tube resonances.

The tube, acting as an acoustical filter, alters the harmonic
content of any sound which passes through it. Changing the
length of the tube cKartgw the r«onanoe pcM'nts and, there-
fore, the tone color of the sound emerging from the opposite
end. Rooms also act as acoustical filters since they affect any
sound made within them.

tn this text, we shall be primarily ^jneeiTii^ with four tHBic

types of filters commonly used in electronic music: the low
pass filter (LPF), the high pass filter (HPF), the band pass
filter (BPF), and the band reject filter. The names imply the
functions. The low pass filter passes low frequencies and
blocks high frequencies, the high pass filter passes high fre-
queneiesv and ^e band pass fitter passes a band or group
of frequencies while the band reject filter rejects a band or
group of frequencies. The most common form of VCF is
the voltage controlled low pass filter. This type of VCF is
so common that when we hear or see the term VCF, it is
usually safe to assume that it is a low pass filter. Many synthe-
sizers also provide a high pass filter; in some systems, this
high pass filter is voltage controlled. Larger systems also
sometimes provide for voltage controlled band pass filtering.

54 The Low Pass Filter

Fig. 5-1 shows the frequency response of a given low pass
filter (LPF). The OdB level is a reference which represents the
nomial output level of the filter when a signal of a given
level is applied at the input. The actual levels involved will
depend on the design of the particular filter. The shading
shows the range and levels of frequencies which can be
passed by the filter. For example, if we apply a 100 Hz
sine wave of the correct level to the Input of the filter,
the output will be OdB, or normal. If we change this sine wave
to 1 ,000 Hz without changing the input level, the output will
be -20dB, or 20dB below the OdB reference level. Again,
changing the sine wave to 11,000 Hz, the output level will
be below — 60dB. This level Is so low in relation to the OdB

Fig. 5-1 LOW Filter

Frequency response Cutof

f point

-10

dB -'0

-30
-•0

/ Cutoff
/ point

-3dB ]

1 100

mnv

Sini

w an 3D

.0 70 ^oa 200 300 no m IAD MOD uoo ftDoo nooo nues
Frequency

reference level that we may consider the 11^00 Hz sine wave
as being missing at the ou^^jt fttter. tn many fitters,
this would probably be below #8 nolle floor of the filter

anyway.

For lower frequencies, the response of the filter is flat; no
matter what the frequency of the sine wave input, the output
will be OdB {assuming the input level remains as before}.
Remember that it requires approximately 3dB difference in
level befbre ^e ear can detect a dffferenee in loudness;
therefore, a sine wave of about 320 Hz, which in Fig, 5-1
produces an output of — 3dB, can be considered the upper
limit of the flat portion of the response. This point on the
filter's curve is called the cutoff point or cutoff frequency;
any frequencies above this point will produce an output level
below -3dB, or levels not as loud a»loM^ fnvtiMi^es. W&h
filters used in electronic rmitte, ^if euttfff ^ almost
always adjustable.

The rate of fall-off of the filter slope js an important con-
sideration because i\ affects ^e relatTve tevels of the fj^
quencies above the cutoff point. The slope is measured by
determining the amount of level change which occurs for
one octave change firfrequency. thfs^measurement is taken
from a portion of the slope which is representative of the
whole. In other words, measuring the slope at the cutoff
point WQiib^ ^ tnaeeurtite slhoe the slope Is curved at this
point, fsbom I^MMJt 500 Hz in Fig. 5-1, the slope falls in a
relatively s|3^(^l line. For a 1,000 Hz sine wave input, the
output level Is ~20dB. A sine wtm one octave above this, or
2,000 Hz, would produce an outptlS of -32dB, an output
level which is 12dB less than the^ivtsine wave. The slope of
filter, then, is -12dB/8va (—11^ decibels per octave).
The minus sign indicates that the slope falls for an increase
in frequency. A plus sign would indicate that the slope rises
for an IncreKe in frequency. The most common filters, at
least as far as electronic music is concerned, are — 3dB,
— 6dB, — 12dB, and — 24dB per octave. Pink noise is usually
generated bY passing vfhite noise through a — 3dB/8va low
pass filter, as shown in Fig. 5-2. -12dB/8va and — 24dB^va
are the most common slopes found in voltage controlled
fitters.

Fig. 5-3 shows the frequency response of what could be

termed the perfect low pass filter because alt frequencies
above the cutoff point are missing from the sound and all
fraquend^ below the cutoff potnt are m the OdB reference
level. In the case of electronic music this type of filter is

probably undesirable.

Up to this point we have been primarily concerned only with
ihe effects the low pass filter on sine waves of given fre-
quencies. In subtractive synthesis we are usually more
interested in the effects of filtering on waveforms rich in
harmmilcs. Fig. 5-4 (a) gives a repetition of the spec^^
diagram for the sawtooth wave. Let us assume a sawtooth
wave with a pitch of Aj (bottom space bass cleft) passed
tiirough a low pass filter with a cutoff point set at about 300
Hz. The results can be shown by superimposing thespectrum
diagram of the sawtooth wave onto the frequency response

Flg.B-2 Nolte Generator

Noise
Source

-3dB/8va
Low
Pan
Filter

■White nt^Mout

•Pink noin out

Fig. ''nrtaet" MMv M Ftltvr

Cutoff point

-40 ' 1 ' I I I M U

FraqMeney

Fig. S-4 Effe^ 0f FIKefing Hatimmics

@ Harmonic contmttif sawtooth wave

-10

-20

dB -30

-40

-SO

-60 I

HARMONIC NUMBER 1 2 3 4 5 6 7 8 9 10 — N

FREQUENCY X 2X St 4X 5X 6X 7X ax gx lOX

D
-1D
-30
-30
-40

-l-n

i-r
t

-1

3ff poin

1 1

1 — 1
H

f
1

■ '

1 1 1 J l\

1 II , 1 ' 1

HARMONIC

1 1 1 1 1

NUMBER

il
il

(

■

«'

BU''

0«

FREQUENCY

curve of the filter, as shown in Fig. 5-4 (b). For comparison,
the dotted lines show the levels the harmonics would reach
without filtering. As can be seen, the first harmonic is not
affected, but all ihe other harmonics are attenuated to one
extent or another. It will be seen in (a) that the normal level
for the fourth harmonic in the sawtooth wave is — 12dB in
relation to the fundamental. According to the filter's response
curve as shown, the output level for a 440 Hz sine wave (the
frequeii^ fourth harmonic) would be — 6dB, in

o'tfier wbrds it would be attenuated by 6dB. The fourth
harmonic, then, is attenuated by 6dB so that its level is— 18dB.
The levels of the other harmonics are affected in a similar
"feshion. Since the levels of the harmonics in the filtered
savirtooth wave are different from the original levels, the tone

color and the shape of the waveform will also be different.

..... 'v ■ :

(Effoets of fiiisring' on waveforms is discus»d in more mml
later in

The Voltage Controlled Low Pan Fitter

It can be seen in Fig. 5-4 (b) that as long as the cutoff point
of the filter remains fixed, the harmonic content of the out-
put sound will remain fixed only if the pitch cif #i#sawtd&^
wave also remains fixed. Changing the pitch of the sawtooth
wave would effectively move the spectrum diagram to the
right or left in relation to the filter response curve, dianging
the harmonic content of the output sound. In other words,
playing a chromatic scale will produce notes each of which
has a different tone color. If we play the pitch of 880 Hz
As (one ledger line above the treble cleft), the level of the
fundamental will have fallen off more than 15dB. Going
mud) higher will considerably reduce the output sound level.

Like the VCO TUNING control, the VCF CUTOFF FRE-
QUENCY control sets the initial cutoff point of the filter,
after which ft can be altered with externally applied control
voltages. If we use the keyboard control voltage output to
control the cutoff point of the VCF. It is possible to cause
the filter cutoff point to follow the pitch. In the example
given in 5-4 above, the filter cutoff point was set at the
approximate frequency of the third harmonic of the 1 10 Hz
As sdWtOO^ WdVB. By applying the pitch control voltage to
the VCF, it is possible to cause the cutoff point to move
with the pitch and remajj^ at the approximate point which
represents the third harmohiccyTany pitch played. From this,
logic would seem to dictate that it would be essential that
the VCF have exactly the same voltage-to-frequency relation
as the VCO. If a change of 1 volt causes one octave change
in VCO pitch, it should also cause one octave change in
the VCF cutoff frequency. With this relation, the VCF can
foltow d^i^ly any flanges in pitch in the music being
played.

The tone color of most instruments changes wi'tti pitch.
Usually the higher pitches are brighter than the lower pitches.
Since high harmonics of high level produce a bright tone
color, this might seem to imply that if a chromatic scale is
played up the keyboard, instead of exactly following the
pftch of the music, the VCF cutoff point should actually
anticipate the pitch by moving higher than normal so as to
allow more harmonics to pass. Instead of 1v/8va it might
seem that something on the order of two octave change
of the cutoff point should occur for 1 volt change in pitch
control voltage. In actual practice, because of the peculiarities
in our heartng, this is not tt6cimt9. In eS(perimenf(ng wf^
1v/8va filters, it will be found that if the pitch control volt^BS
is attenuated by approximately half, the tone color of the
output sound wilf seem to our ears to retain an approxfmately
constant harmonic c(»¥|efit if the pitch control voltage in
not attenuated, the tone color will seem to get brighter with
higher pitches. A response Of iMra fiMitits vfitid.

The tone eotdf 0f many instruments, especially wind instru-
ments and plucked strings, changes during the production of
each note. This can be imitated by using an envelope genera^
tor to cause the VCF cutoff pointto change. ©fHm^itaf

envelope which is used to control the VGA can also beim^'
to control the VCF. In other cases, it is advantageous to u^ a

56 Timbre

second envelope generator so that the sweep of harmonics
is independent of the loudness contour. Some synthesizers
allow tm^i^ion 6f tftg dnvtlope so tiiat the harmonics can
sweep in the opposite direction from what is nortrtalty
expected.

Another common source of modulation fiar the VCF h ite
LFO. whidi produces a wavering of the tone color c^ed
growl.

5-6 The High Pass Fitter

The high pass filter (HPF) may be thought of as an «Xaet,
mirror image of the low pass filter. Fig. 5-5 (a) shows '^e
frequency response of a high pm filter viAth a $I0|» of 12dB/
octave. In (b) is shown the spectrum dia{NWn of 8 sawtooth
wave superimposed on the response curve of ^e filter. In this
flxamplft, ^e frequency ^« sawtooth wave is 1 10 Hz and
the cutoff point of the filter is set at about 770 Hz which is
the frequency of the seventh harmonic of the sawtooth wave.
The smmitfi haitnorilc is Hhia sirorigsit, while ftmdwnantal
is attenuated by almost 35dB. The third harmonic is normal-
ly 9.5dB lower than the fundamental. It is attenuated by
16dB due to the filter's slope so that its level becomes
-24.6dB.

Fig. 5-B HlghPaw BHBF
(§) Frequency response

Cutoff point

}

t ■

■ 1-

n JOB Mt no Mw -
FREdUENCV

aoo aw no na vm'
FREQUENCY

Experiments have shown that if the ear is simultaneously
given a series of overtones which fall within the natural
hannonic series, it wi!t h^r ^e fundahfidrital pitelh even ff
the fundamental is completely missing from the series. This
explains the 16 Hz organ pitch shown in Fig. 1-2 which falls
below *e normal f»«c(ueney range the ear. The ear hears
all the harmonics which are within its normal range and
"mentally" furnishes the fundamental which is too low to
hear. This phehomehon alto ex^^tw why a sdU'nd with averi
a great amount of high pass filtering usually does not lose
its previous pitch sense.

Since high pass filters block lower frequencies, they are often
used to brlghtsn sy»lhestz«d soun^. Soma synthesizers
include voltage eontrdlled high pass filters.

The Band Pass Filter and Band Reject Filter

The band pass filter (BPF) passes a band or group of frequen-
cies. The average band pats ffltarhasa naritnv band wld^ as
shown by the response curve in Fig. 5-6 (a), the only dif-
ferences being in the slopes. In this example, the center fre-
quency of the filter Is 1^0 Hz so that fi^uenelM higher
and lower than this will be attenuated. The response for a
wide band pass filter is shown in (b) (next page). In this filter,
the response between the upper and low«r l^tts tt flat A
wide band pass filter of this type can be made by (IMII^Inga
low pass filter in series with a high pass filter as Aown Ih (c).
In this case, the control of the upper and lower Hfflfts m
independent of each other so that the limits may be set at
any desired point.

Fig. SS Band Pan Filters

(a) Narrow bandwidth

FREQUENCY

SB TiiAbre

(Fig. 5-6)

(g) Wide bandwidth

dB -»

3dB

—3 dB

4—

FReaUENCY

HPF Response

BPF Response

Low

Pass

Filter

High

Pass
Filter

GUT

The result will be
the same if the
two filters are
reversed

The band reject filter is an inversion of the band pass filter,
as ^own in Fig. and can be made by patching a low pass
filter in parallel with a high pass fil^i: as shown in (c).

Effectt of filtering on Waveforms

It is of a certain value to demonstrate the effect that filtering

lias on a given waveform. For this, the square wave is ideal
twcause it contains the extremes of both high and low fre-
quency (»mponents. High frequencies are characterized by
rapid changes in voltage level. In the "perfect" square wave,
the vertical edges would be instant changes in voltage, an
impossibility since they would then represent a frequency of
infinity. Even a medium quality square wave, however, will
produce vertical edges which would be equivalent to very
high frequencies. Low frequencies are characterized by slow
(from the audio point of view) changes in voltage. The
horizontal portions of tiie "perfect" square wave would
represent zero Hertz (DC voltage, or no dtjanges).

Fig. 5-8 (b) shows what happens to a square wave when it is
passed through a low pa^ filter. The tow pasa filter can be

Timbre 59

Fig. 5-7 Band Rejeet i^tesnt
0 Ntlrtowbaindwidflfi

} dB

dwidth—

'4i 4) N M M> m Me 100 TOO iju vm xooo
'FREQUENCY

MOO TMS lOAM

(b) Wide bandwidth

-3cl

10 in 30 u ro 100

300 300 goo no ijxn imo voa »mo i.mo io^

FREQUENCY

LPF Response +

IN-

HPF Response

Band Reject response

Low
Pass
Filter

High
Pass
HIter

OUTPUT

60 Timbre

5-9

thought of as being slow and sluggish, resisting fast changes.
This tendancy causes the output of the filter to lag behind
tfie quick changes in the square wave, softening the comers
of the squares. The lower the cutoff frequency of the filter
in relation to the frequency of the square wave, the more
pronounced the softening of the high frequency component
vertical edges will be. Notice that with the cutoff point low
in relation to the input frequency, the square wave begins to
toolc very much like a triangle or sine wave, indicating the
supression of the upper harmonics.

Fig. 5-8 (c) shows what happens to a square wave when it is
|^$ed through a high pass filter. The high pass filter can
react very quiclcly to sudden changes in a wavefomi, but
it can be thought of as being very poor at holding fixed levels
as occur in the horizontal portions of the square wave.
Since these horizontal portions cannot be hieild. they tend
to fall back towards the zero level; the higher the cutoff
point of the filter, the faster these horizontal levels return to
the zero tevel. With Ifie cutoff point viary high, the filter pro-
duces a waveform with only sharp spikes since it effectively
passes only the high frequency vertical portion of the square
wave and blodcs all of tfta hcMrteontat touf':;fi9fipieney portions.

The eontrol voltage output of the keyboard controller Is

very much like a square wave In that when a series of pitches
is played, the output voltage makes very quick jumps up or
down to each new level. Fig. 5-9 (a) shows the trontrol voltage
output for a chromatic scale. In (b) is shown what happens
to this control voltage when we add the effect of portamento.
'Ihis demonstratas the faet tl^at the portamento dibits are

basically nothing more than a tow pass filter applied to the
keyboard control voltage output. If we play a trill on the
keyboard, the control voltage output will be a tow frequency
square wave. Using various depths of portamento will produce
waveforms exactly as shown in Fig. 5-8 (b), the only dif-
ference Isaing that the related frequencies would be much
lower. The frequency produced by even a very rapid trill
on the keyboard is very low compared to ordinary audio
frequencies. Most filters, except of course thosa desifhed to
produce portamento effects, have a low frequency limit
which would be far above these keyboard "frequencies" so
that ev«i a low pass^ter would act as a high pass filter on
the keyboard eormidlVdiltage output

Resonance in Filters

In aleetfoniM, feedback refers to fhe frading of a portion of

the output signal of a device back into the Input of the same
device. The result will depend on whether the feedback is
pdsltiva or n<^aUva.

In negative feeicttiaak, tha polafify dr phase of '^a-feedbaek

signal Is opposite the polarity or phase of the input signal;
the result is a dampening of the input signal. Many audio
amplifiers use negative feedback intemalty. Tlie n^f^^
feedback tends to cancel out distortion and noise which occur
within the amplifier, thus improving the quality of reproduc-
tion.

Fig. 5^ Eftoeti of Filttring on WaviEifdrms
@ Square wava

@ Low pass filtering

Freq

high

CO
Freq
medium
high

CO
Freq
mecBum
low

Pi«q|

Low

CO
Freq

tow

CO
Freq
medium
low

Freq

mKUym

Fraq

high

Timbre 61

Fig. 5-9 Keyboard Portamento

Keyboard control voltage ou^t for chrometic scale

Voltage
6/12

@ Portamento

5/12
4/12
3/12
2/12
1/12

1/12 i— '

Time

In potittve fMidbMik, ftddbadc signal is of thd same

polarity or phase as the input signal. The feedboelc signal
reinforces the input signal. It is easily possible fer this
positive feedback signal to reirjfbrce the Input so much ijnttt
self-oscillation occurs. The classic example of ^fs Is the
howling PA system in which sound from the Sjiraksr re*
enters the microphone to b« aimpHfldd^ dv6r arid t/m ogain.
Many types of electronic oscillators use pdSltEve fetfdbttok to
produce oscillations.

Resonance in filters is produced by inducing positive feed-
'beck. In many fitters, espedaltV ^e vOhsge controlled type,
the amount of feedback is adjustable. The control for this
purpose might be labelled: RESONANCE, EMPHASIS, or
sometimes simply '^d" f'Q" H a factor used in measutln9
ci^cuft resonances), but All of themptflfmthfrsfihe function.

Fig. 5-1 1 shows a simplified block diagram of how feedback
is applied inside a voltage controlled filter. For frequencies at

Fig. 5-10 Positive Feedback in a PA System

6 ooooO

Amplifier

Fig. S.11 VGF Retonenee Btetsk Df^lfeMt

Resonance

control

Input

VCF

Output

Waveforms show the phase relatitmsforfmiuendesatthe
cutoff point of the filter.

62 Timbre

Fls.S-12 VCF (Low Pass) Resonance
(g) Small amount of mona nce

(30

dB -ID

-JO

10 lOM se 70 tsa «biaii M4dii tm u» moo mso 7i« nuoa
Medium amount df mdiMTiea

•10

-IB

30 30 ■)»« an9»il»las im un son uoa tm> torn

PREOUENCY

(But not enough to produce oscillations).

*I0

-10
-30

10 3030 airano ^ mt. ^ t/m tM a^no am ijm tofito

64 Timbre

S-10 Ringing In Filters.

In Chapter One it was stated that: Resonance occurs when-
ever a body or system is set into vibration at its own natural
frequency as a result of impulses received from a body or
system vibrating at the same frequency. Returning to the
analogy of the child's swing, if the swing is hanging motionless
and a single impulse or push is given to the swing, it will
begin to swing at its natural frequency or period, after which
it will slowly die to a motionless state again. A filter with
resonaniM reacts in a similar way to impulses supplied by the
waveform at the input of the filter. This type of reaction is
called ringing.

Fig. 5-14 shows what happens to a square wave apptfed to a
filter with various degrees of resonance. Note that due to
positive feedback, the vertical edges of the square wave
overshoot their normal level, then waver up and down as
they try to settle to the correct level. The frequency of
tiiese wavarir^ is determined by the cutoff point of the
filter. The wawform at (e) will of course occur whether
there is an input waveform or not (the oscillations will
begin as a rasult of internal circuit noise) and the frequency
will be ^at of ^ cutoff firequency of the Alter.

5-11 The Basic Synthesizer Patch

Fig. 5-15 shows the completed basic synthesizer patch.
This is the most common arrangement used to produce

sounds. The variations possible on this patch are almost
limitless. One of the most common variations is to use more
*than one module or alemanl For mample, with nutnv
sounds it is better to USB more than one VCO and/or mor«

than one VCF.

The VCF is a dynamic filter since, due to control voltages
acfing on it. Its characteristics often change durfng the
production of each note. Often it is desirable to simultane-
ously ihflt^te the tone colors which do not change. This can
be done by means of a itatlc fliter, a fitted whose character*
istics remain fixed once it has been set by means of its front
panel controls. Such a filter would normally be added between
the VGF wid VGA.

Fig. 5-14 Effects of Resonance on Waveform
(a) Nomonanee

® Ria^«M low

@ Resonance
high

Q Self

oscillation

fr = Cutoff frequency of filter

Timbre 65

66 Timbre

5-12 QuMtilMii

1. What K the diffsrancebMem a white noise ami #pmk^ ^

2. What are the four types of filter comnmnty u$ed in electronic music? What are their basic functions?
3; How the tiutsff 0«HTft of s f^vst det^lmd^

4. What does it mean when we say a given filter has a fall off rate of -24dB/8va?

5. Why is it necessary soUnattrntts to control the cutoff point of the filter with the keyboard control voltage?

6. In a synthesize wi^ 1v/8va exponential VCCs, what voltage-to-frequency relation ^outd be used for the
filfsf^Why?

7. In a sound with a high amount of high pass filtering, the lower harmonics are effectively missing from the
output sound. Why does the output sound stUI retain its sense of pitch?

8. Make diagrams of the effects of low pass and high pass filtering on a square wave.

9. How is resonance induced in a filter? How does it affect the filter's frequency response curve? How does it
affect a square wave?

10. What is ringing in a filter? What affect does filter ringing have on a square wave input?

Words to define:

band pass filter
band reject filter
BPF

cutoff frequency

feedback

filter

filter slope
growl

high pass filter

HPF

low pass filter
LPF

negative feedback

noise

oscillation

pink noise
positive feedback
resonar«» (filter)
ringing (filter)
self-oscillation
VCF

voltage controlled filter
white noise

Metric Conversion Table

The conversion table below allcM^ ^ifiek and eaiy comMoti from one metifG prefTx to another^ The prefixes

listed are those which are commonly used in electronics and electronic music. To use the table, find the given
prefix in the column on the left, then follow the line horizontally to the vertical column containing the desired
pnt^ The figuif indicates the number of places the dedmid point must be movetf and the arrow thdibates the

EXAMPLE: Convert 3 kHz to units (Hz). (3 kHz = 3 kilohertz.) Find "kilo" in the left-hand column; move to the
right to the vertical column headed "units". 3 => indicates that the decimal point must be moved three places to
the right, thus:

3 kHz = 3,000 Hz

EXAMPLE: Convert 380 milliseconds to seconds. Find "milli" in the left column: to the right, under "Units",
readt^-S, tiius:

3B0 mnilseeonck = 0.38 sisoond

Metric Coiwariion Tiitole

ORIGINAL
VALUE

DESIRED VAL

Mega

Kilo

Units

Deci

Centi

Milli

Micro

Micromicro

Mega

3=>

6 =>

7 =>

9=>

18=>

Kilo

^ 3

4=>

5=^

6=>

9=>

15=*

Units

<- 6

1 =»-

2=>

3«*

12*

Deci

*■ 7

4-4

^ 1

1 ^

5=»-

11«*

Centi

<= 8

^ 5

<= 2

<= 1

I-"

4 =>

10=>

Milli

•= 3

<= 2

<= 1

3 =>

Micro

<=12

«= 9

^ 6

^ 5

Pico

*«1S

•0-12

••=10

Index

Additive lyn^Mtilft, flB^

ADSR,44

AM. 47

Amplifier, summing, 35

voltage controlM, 20,44
Amplify, 14

Amplitude modulation. 47
Anechoic chamber, 39
Anilnode, 6

Attacl< time (A), 44
Attenuate, 14, 35

Band pass filter (BPF), 52, 57
Band reject filWR4.^,68
Bar, 39

Basic lynthesteAf mnitt ^ 38. 48, 65
Beat, 29

Beat frequency, 29

Bell, Alexander Graham, 39

BPF, 52, 57

Cent, 32

Central proceMlnS UAH tGPU},22
Chord, 27
Chorus effect, 10
Clarinet, waveform of, 16
Comprenion {cA str). 2
Computer music, 20-24
Concord, 27
Consonance, 27, 30
Control response of VGA, 45

of VCF,55

of VCO, 32-36
Control voltage, 19
Cutoff frequency, filter, 53
Cutoff point, f lltw^, 63

dB,39

dB SPL,40

Decay time (D), 44

Decibel, 39

Direct synthesis, 23

Discord, 27

Dissonance, 27, 30

Dyck, Ralph, 22

Dynamic filter, 84

Dynamic mtmA%^

Dyhamt(^8,39

Echo, 9

Electronic music, 13-14

live, 13

recorded, 14
Emphasis, 61
End correction, 3
Envelope, 8, 44

organ, 44

piano, 8, 44, 45

synthesizer, 44

vowel sound "ah", 8
Envelope generator, 44
Equal temperament, 28
Even temperament, 28
Exponential decay, 45
Exponential generator, 34
Exponential progression, 31-^2
Exponential VCA, 46
Exponentia) VCO, 33

Feedback, negative, 60

positive, 61
Filter, 16, 51

band pass, 52, 57
- band reject, 52, 58

cutoff frequency, 53

frequency response of, 62, 56€9, 62

fall off rate, 53

dynamic, 64

effects of resonance, 63

effects on waveform, 58, 60

high pass, 52, 56

low pass. 52-56, 60

pink noise, 53

ringing in, 64

slope, 53

Btetlc.64

voltage controlled, 19, S%.S6S$
Flute, spectrum of, 15
waveform of, 1 6

FM,36
Frequency, 1

Frequency modulation (FM), 36
Frequency response of ear, 2, 40-41

of filter, 52
Fundfu^Bntal, 5

Gate pulse, 44, 47
Growl, 56

Guitar, 6, 8
Harmonics, 5, 29
first, 5

intensity of, 8,42

inversion of, 18, 19

second, 5
Harmonic series, natural, 6, 30
Harmony, 27
Hearing, threshold of, 39
Hertz (Hz), 2
Hertz, Heinrich Rudolf, 2
High pass filter, 52. 56-57
Hold control (VCA), 47
HPF,62,6667

Initial gain, 47
Intensity, 40

of hamionics, 8, 42
Interval, 27

consonance and dissonance of, 30

Just intonation, 28

LFO,36,47, 56
Linear scale, 31
Linear VCA, 45
Linear VCO, 32. 33
Loudness. 8, 39, 40

Low frequency oscillator (LFO), 36,47. 56

control of VCA, 47

control of VCF, 56

control of VCO, 36
Low pass filter (LPF), 52-56.60

control response of, 55

cutoff frequency, 53

perfect, 53

voltage controlled, 55-56
voltage-to^requency relation, 55
LPF {see Low pass flltier)

Index 67

Microbar (^ibar), 39
MicroComposer, 22
Microprocessor, 22
Modulation, 19,36

amplitude, 47

frequency, 36
Monochord, 3-4
Music, computer, 20t24

electronic. 13-14

scale systems, 28
Musique concrete, 1 3

Natural harmonic series, 5, 30
Negative feedback, 60
Node, 6

Noise, 20, 42, 51
pink« 20,51. 53

w ov f o i m of.go

white, 20, 51
Noise generator, 20, 42, 53
Noti^Mmionie overtones. 7

Octave, 27
Oscillator, 16, 19,27

exponential, 33

linear, 32, 33

low frequency, 36.47, 56

voltage controlled, 19> 27
Overtones, 4. 29

non-harmonle, 7

Patching, 19
Pendulum, 14-15
Phase, 18, 60
Phase shifter, 10, 18
Phon,41

Pickup (gultBr),positton,;a^ 6
Pink noise, 20.51,53
Pink noise filter. 53
Pipe, closed end, 3

open end, 3

scale of, 7
Pitch, 1 , 27
Polarity, 60
Portamento, 60
Positive feedback, 61

f^toil«flBte,44^47

0*61

Ramp wave, 16
Rarefaction, 2
Releese time, (R ), 44
Resonance, body Onsti'ument). 7

dffined,2,64

effect on waveform, 64

frequency response In f ilttrs, 62, 63

in closed end air eolur^Si'^

in filters, 61

in open air cotumns, 3

in strings, 3-4
Resonance tubes, 3
Response, filter frequency, 52
Response, VCA control, 45

VCF control, 55

VCO control, 32-36
RevertKration, 9
Ringing in filters, 64
Roland MC-8 MicroComposer, 22

68 Index

Sawtooth wave, 16-18,
inversion of, 18

spectrum of, 17, ■s'
waveform of, 1 7
Scale, comparison of linear 9(Kl'^N)0nentiat. 32

Krwftr.SI

musical, 28
Scale of pipe, 7
Self-oscillation, 61, 63
Sine wave, 14, 60,63

inversion of, 18
Sonometer, 3-4
Sound, 1

defined, 1

•peed of, 2

three qualities of, 1
Sound pressure level (SPL),40
Sound waves, 2

propagation of, 8
Spatial effects, 10
iG^ctrum diagrams, 16

effecu of filtering, 64, 56. 63

of clarinet, 16

of flute. IS

of sawtooth wave, 17,

of square wave, 17, 43

of triangle wave, 43

of trumpet. 16
SPL.40

Bquare wave, 16, 42. 68

inversion of, 18

spectrum of, 17^^
Static filter, 64

Subtractive synthesis, 16, 1&-20; S3t
Summing amplifier. 36
Sustain, (S),44
Svntfiesis. 16, 19

additive, 16

direct, 23

subtractive, 16. 19-20, 53
$yfiimj»F, barie patch, ig, 35, 48, 65
eofn^w ooncpol of, 22
vdttaoB «onirolled, id

Threshold of hearing, 39
Threshold of pain, 39
Timbre, 4, 51
Tone color, 4, 51

changes with pitch, 20, 55
Transient generat!W,44
Tremolo, 47
Tittantf a wave, 42, 60

spectrum of, 43

wjaveform of, 43
Trumpet, spectrum of, 15

waveform of, 15

TMningM^'t^a4,i4

UrtiS(Hl,27

VCA (see Voltage controlled amplifier)
VCF isee Voltage controlled filter)
VCO isee Voltage oottOe^ OldUator}
Vibrato. 36

V^t^^ntrolled amplifier (VCA), 2D, 44
control by LFO, 47

control response, 45
exponential, 46
linear, 45

Voltage controlled filter (VCF). 19,51,55-56

control by LFO, 56

conttvl mponse, 56

cutelf frnqiian^, 83

frequency ravMHW,^
Voltage cbmir6llM«sdUfltt0)- fVCO), 19, 27

control by LFO, 36

control response, 32-34

exponential, 33

linear, 32, 33
Voltage eontrollsci «|nnl»^>Mf^10

ari^lituda niodiilMed. 47
clarinet, 15
effect of filtering, 58
effect of resonance, 64

electrical, 14
flute, 1 5

frequency nradulated, 36
houshold electricity, 15
f»l«,20
Hiwtemh,i7

sine wave, 14

square wave, 1 7, 43, 60, 64

triangle wave, 43

trumpet, 15
Wavelength, 2
White noise, 20, 51

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